The notion of a fork appears in the characterization of graph mathematics graph s, including network topology , and topological space s. image 6n graf.svg thumb A graph with forks in vertices 2, 4, and 5. A graph has a fork in any vertex graph theory vertex which is connected by three or more graph theory edges . Correspondingly, a topological space is said to have a fork if it has a subset which is homeomorphic to the Glossary of graph theory Graph topology graph topology of a graph with a fork. Stated in terms of topology alone, a topological space X has a fork if X has a Closed set closed subset T with connected space connected Interior topology interior , whose Boundary topology boundary consists of three distinct elements and for which the boundary of the complement set theory complement of T s interior relative to X consists of these same three elements. It is perhaps worth noting that certain definitions of a Curve Simple curve simple curve as Map mathematics map c I X of a Real number real valued interval I to a topological space X such that c is continuous function topology continuous and injective with the exception, for closed curves, of the two interval endpoints are Strength mathematics weaker than the requirement that its range X be a connected topological space without forks. topology stub Category Topological graph theory ... more details
A M bius strip , an object with only one surface and one edge. Such shapes are an object of study in topology. Topology from the Greek language Greek , place , and , study is a major area of mathematics ... . This later acquired the modern name of topology Specify . By the middle of the 20 sup th sup century, topology had become an important area of study within mathematics. The word topology is used both ... to define a topological space , a basic object of topology. Of particular importance are homeomorphism ... inverse . For instance, the function y x sup 3 sup is a homeomorphism of the real line . Topology includes many subfields. The most basic and traditional division within topology is General topology point set topology , which establishes the foundational aspects of topology and investigates concepts inherent to topological spaces basic examples include compactness and connectedness algebraic topology ... groups and homology mathematics homology and geometric topology , which primarily studies manifold ... dimensional topology and graph theory , do not fit neatly in this division. Image Trefoil knot arb.png ... Knot theory studies knot mathematics mathematical knot s. See also topology glossary for definitions of some of the terms used in topology and topological space for a more technical treatment of the subject ... problem solved by Euler. Topology began with the investigation of certain questions in geometry ... ref is regarded as one of the first academic treatises in modern topology. The term Topologie was introduced ... had used the word for ten years in correspondence before its first appearance in print. Topology ... chiefly are treated . The term topologist in the sense of a specialist in topology was used in 1905 ... corresponds exactly to the modern definition of topology. Modern topology depends strongly on the ideas ... part of algebraic topology . Maurice Fr chet , unifying the work on function spaces of Cantor, Vito ... 2010 For further developments, see point set topology and algebraic topology . Elementary introduction ... more details
Other uses File assorted forks.jpg right thumb Assorted forks. From left to right dessert fork, relish fork, salad fork, dinner fork, cold cuts fork, serving fork, carving fork. File BlauweVork.png right thumb Blue Fork Sillhouette As a piece of cutlery or kitchenware , a fork is a tool consisting of a handle with several narrow Tine structural tines on one end. The fork, as an eating utensil, has ... function, in the Fork etiquette American style American style of fork etiquette, the fork ... , the fork is held with the tines curving down. Citation needed date November 2010 A fork is also ... century. The word fork comes from the Latin furca , meaning pitchfork . The ancient Greeks used ref ... the fork as a serving utensil, and it is also mentioned in the Hebrew Bible, in the Book of I Samuel ... s servant came, while the fresh flesh was boiling, with a fork of three teeth in his hand... . However ... Journal comments 310 311, pl. xlix ref Before the fork was introduced, Westerners were reliant on the spoon .... The tines on these implements were straight, meaning the fork could only be used for spearing food and not for scooping it. The fork allowed meat to be easily held in place while being cut. The fork ... consuming it. Wider use of the table fork in Western Europe was facilitated by two Byzantine imperial ... Selvo , in 1075. Citation needed date July 2010 By the 11th century, the table fork had made its way ... and upper classes by 1600. It was proper for a guest to arrive with his own fork and spoon ... s entourage. Long after the personal table fork had become commonplace in France, at the supper ... is presented with a splendid Fork Holder. The fork s adoption in northern Europe was slower ... rodmur sca fork.html title A History of the Table Fork ref ref cite web url http www.geocities.com ... Dining Etiquette.html archivedate 2009 10 27 ref It was not until the 18th century that the fork ..., England and Sweden already by the early 17th century. ref http www.bookrags.com research knife fork ... more details
In functional analysis and related areas of mathematics the strong topology is the finer topology finest polar topology , the topology with the most open set s, on a dual pair . The coarser topology coarsest polar topology is called weak topology polar topology weak topology . Definition Given a dual pair math X,Y, langle , rangle math the strong topology math beta Y, X math on math Y math is the polar topology defined by using the family of all sets in math X math where the polar set in math Y math is Absorption law absorbent . Examples Given a normed vector space math X math and its continuous dual math X math then math beta X , X math topology on math X math is identical to the topology induced by the operator norm . Conversely math beta X, X math topology on math X math is identical to the topology induced by the norm mathematics norm . Properties In barrelled space s the strong topology is identical to the Mackey topology . mathanalysis stub Category Topology of function spaces ... more details
Unreferenced date December 2009 In functional analysis and related areas of mathematics the weak topology is the coarser topology coarsest polar topology , the topology with the fewest open set s, on a dual pair . The finer topology finest polar topology is called strong topology polar topology strong topology . Under the weak topology the Bounded set topological vector space bounded set s coincide with the relatively compact set s which leads to the important Bourbaki Alaoglu theorem . Definition Given a dual pair math X,Y, langle , rangle math the weak topology math sigma X,Y math is the weakest polar topology on math X math so that math X, sigma X,Y simeq Y math . That is the continuous dual of math X, sigma X,Y math is equal to math Y math up to isomorphism . The weak topology is constructed as follows For every math y math in math Y math on math X math we define a semi norm on math X math math p y X to mathbb R math with math p y x vert langle x , y rangle vert qquad x in X math This family of semi norms defines a locally convex topology on math X math . Examples Given a normed vector space math X math and its continuous dual math X math , math sigma X, X math is called the weak topology on math X math and math sigma X , X math the weak star topology weak topology on math X math DEFAULTSORT Weak Topology Polar Topology Category Topology of function spaces ... more details
In mathematics , a strong topology is a topology which is stronger than some other default topology. This term is used to describe different topologies depending on context, and it may refer to the final topology on the disjoint union topology disjoint union the topology arising from a normed vector space norm the strong operator topology the strong topology polar topology , which subsumes all topologies above. Note that a topology is stronger than a topology is a Comparison of topologies finer topology if contains all the open sets of . In algebraic geometry , it usually means the topology of an algebraic variety as complex manifold or subspace of complex projective space , as opposed to the Zariski topology which is rarely even a Hausdorff space . See also Weak topology mathdab Category Topology ... more details
of hops between two nodes, is a hypercube . The number of arbitrary forktopology forks in mesh networks ... topologies. Network topology is the layout pattern of interconnections of the various elements Data ...?id 3516 title network topology author ATIS committee PRQC publisher Alliance for Telecommunications ... may be physical or logical. Physical topology means the physical design of a network including the devices, location and cable installation. Logical topology refers to how data is actually transferred in a network as opposed to its physical design. In general physical topology relates to a core network whereas logical topology relates to basic network. Topology can be considered as a virtual shape ... not necessarily mean that it represents a ring topology. Any particular network topology is determined ... nodes. The study of network topology uses graph theory . Distances between nodes, physical interconnections ... topology and a logical topology. Any given node in the LAN has one or more links to one or more ... that may be used to describe the physical topology of the network. Likewise, the mapping of the data flow between the nodes in the network determines the logical topology of the network. The physical and logical topologies may or may not be identical in any particular network. Basic topology types The study of network topology recognizes seven basic topologies ref name Bicsi, B. 2002 Bicsi, B., 2002 ... topology Bus point to multipoint topology Star topology Ring topology Tree topology Mesh topology Hybrid topology This classification is based on the interconnection between computers be it physical or logical. The physical topology of a network is determined by the capabilities of the network ... the physical topology of the network. This refers to how the cables are laid out to connect many computers to one network. The physical topology you choose for your network influences and is influenced ... used Logical topology describes the way in which a network transmits information from network computer ... more details
In mathematics , the uniform topology on a space has several different meanings depending on the context In functional analysis, it sometimes refers to a polar topology on a topological vector space. In general topology, it is the topology carried by a uniform space . In real analysis, it is the topology of uniform convergence . Disambig ... more details
Unreferenced date December 2009 In functional analysis , a branch of mathematics , the ultraweak topology , also called the weak topology , or weak operator topology or weak topology , on the set B H of bounded operator s on a Hilbert space is the weak topology weak topology obtained from the predual B sub sub H of B H , the trace class operators on H . In other words it is the weakest topology such that all elements of the predual are continuous when considered as functions on B H . Relation with the weak operator topology The ultraweak topology is similar to the weak operator topology. For example, on any norm bounded set the weak operator and ultraweak topologies are the same, and in particular the unit ball is compact in both topologies. The ultraweak topology is stronger than the weak operator topology. One problem with the weak operator topology is that the dual of B H with the weak operator topology is too small . The ultraweak topology fixes this problem the dual is the full predual B sub sub H of all trace class operators. In general the ultraweak topology is more useful than the weak operator topology, but it is more complicated to define, and the weak operator topology is often more apparently convenient. The ultraweak topology can be obtained from the weak operator topology as follows. If H sub 1 sub is a separable infinite dimensional Hilbert space then B H can be embedded in B H H sub 1 sub by tensoring with the identity map on H sub 1 sub . Then the restriction of the weak operator topology on B H H sub 1 sub is the ultraweak topology of B H . See also Topologies on the set of operators on a Hilbert space ultrastrong topology weak operator topology DEFAULTSORT Ultraweak Topology Category Topology of function spaces Category Von Neumann algebras ... more details
In any domain of mathematics , a space has a natural topology if there is a topology on the space which is best adapted to its study within the domain in question. In many cases this imprecise definition means little more than the assertion that the topology in question arises naturally or canonically ... . For example, if Y is a subset of a total order totally ordered set X , then the ml Order topology Induced order topology induced order topology , i.e. the order topology of the totally ordered Y , where this order is inherited from X , is coarser than the subspace topology of the order topology of X . Natural topology does quite often have a more specific meaning, at least given some prior contextual information the natural topology is a topology which makes a natural map or collection of maps Continuous function topology continuous . This is still imprecise, even once one has specified ..., there is often a finest topology finest or coarsest topology coarsest topology which makes the given maps continuous, in which case these are obvious candidates for the natural topology. The simplest cases which nevertheless cover many examples are the initial topology and the final topology Willard 1970 . The initial topology is the coarsest topology on a space X which makes a given collection of maps from X to topological spaces X sub i sub continuous. The final topology is the finest topology ... topology on a subset of a topological space is the subspace topology . This is the coarsest topology which makes the inclusion map continuous. The natural topology on a quotient space quotient of a topological space is the quotient topology . This is the finest topology which makes the quotient map continuous. Other examples include the topology induced by the Helly metric . References cite book last Willard first Stephen title General Topology publisher Addison Wesley, Massachusetts year ... category Topologytopology stub ... more details
Unreferenced date December 2009 In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a dual pair , two vector space s with a bilinear form defined on them, so that one vector space becomes the continuous dual of the other space. The different dual topologies for a given dual pair are characterized by the Mackey Arens theorem. All locally convex topologies with their continuous dual are trivially a dual pair and the locally convex topology is a dual topology. Several topological properties depend only on the dual pair and not on the chosen dual topology and thus it is often possible to substitute a complicated dual topology by a simpler one. Definition Given a dual pair math X, Y, langle , rangle math , a dual topology on math X math is a locally convex topology math tau math so that math X, tau simeq Y. math That is the continuous dual of math X, tau math is equal to math Y math up to linear isomorphism . Properties Theorem by George Mackey Mackey Given a dual pair, the bounded set topological vector space bounded set s under any dual topology are identical. Under any dual topology the same sets are barrelled set barrelled . Characterization of dual topologies The Mackey Arens theorem , named after George Mackey and Richard Friedrich Arens Richard Arens , characterizes all possible dual topologies on a locally convex space s. The theorem shows that the coarser topology coarsest dual topology is the weak topology , the topology of uniform convergence on all finite subsets of math X math , and the finer topology finest topology is the Mackey topology , the topology of uniform convergence on all weakly compact subsets of math ... and math X math its continuous dual then math tau math is a dual topology on math X math if and only if it is a topology of uniform convergence on a family of absolutely convex and weak topology weakly compact subsets of math X math DEFAULTSORT Dual Topology Category Topology of function spaces ... more details
nofootnotes date September 2010 In functional analysis , the ultrastrong topology , or &sigma strong topology , or strongest topology on the set B H of bounded operator s on a Hilbert space is the topology defined by the family of seminorms p sub w sub x for positive elements w of the predual L H sub sub of trace class operators. The seminorm p sub w sub x for w positive in the predual is defined to be w x sup sup x sup 1 2 sup . It was introduced by von Neumann in 1936. Relation with the strong operator topology The ultrastrong topology is similar to the strong operator topology. For example, on any norm bounded set the strong operator and ultrastrong topologies are the same. The ultrastrong topology is stronger than the strong operator topology. One problem with the strong operator topology is that the dual of B H with the strong operator topology is too small . The ultrastrong topology fixes this problem the dual is the full predual B sub sub H of all trace class operators. In general the ultrastrong topology is better than the strong operator topology, but is more complicated to define so people usually use the strong operator topology if they can get away with it. The ultrastrong topology can be obtained from the strong operator topology as follows. If H sub 1 sub is a separable ... with the identity map on H sub 1 sub . Then the restriction of the strong operator topology on B H &otimes H sub 1 sub is the ultrastrong topology of B H . The adjoint map is not continuous in the ultrastrong topology. There is another topology called the ultrastrong sup sup topology, which is the weakest topology stronger than the ultrastrong topology such that the adjoint map is continuous. See also Topologies on the set of operators on a Hilbert space ultraweak topology strong operator topology ... 3AOACTFR 3E2.0.CO 3B2 S On a Certain Topology for Rings of Operators The Annals of Mathematics 2nd Ser., Vol. 37, No. 1 Jan., 1936 , pp. 111 115. Category Topology of function spaces Category von Neumann ... more details
Infobox Book name Counterexamples in Topology image image caption author Lynn Steen Lynn Arthur Steen ... Counterexamples in Topology 1970, 2nd ed. 1978 is a book on mathematics by topology topologist s Lynn ... a counterexample which exhibits one property but not the other. In Counterexamples in Topology , Steen ... , Minnesota in the summer of 1967, canvassed the field of topology for such counterexamples and compiled ... space which is not second countable space second countable is counterexample 3, the discrete topology ... of metrization theory and general topology see History of the separation axioms for more. List of mentioned counterexamples colbegin cols 2 finite set Finite discrete topology Countable discrete topology Uncountable discrete topology Indiscrete topology Partition topology Odd even topology Deleted integer topology Particular point topology Finite particular point topology Particular point topology Countable particular point topology Particular point topology Uncountable particular point topology Sierpinski space , see also particular point topology Closed extension topology Finite excluded point topology Countable excluded point topology Uncountable excluded point topology Open extension topology Either or topology Finite complement topology on a countable space Finite complement topology on an uncountable space Countable complement topology Double pointed countable complement topology Compact complement topology Countable Fort space Uncountable Fort space Fortissimo space Arens Fort space Modified Fort space Euclidean space Euclidean topology Cantor set Rational number s Irrational ... topology One point compactification of the rationals Hilbert space Fr chet space Hilbert cube Order topology Open ordinal space 0, where Closed ordinal space 0, where Open ordinal space 0, Closed ordinal space 0, Uncountable discrete ordinal space Long line topology Long line Long line topology Extended long line An altered Long line topology long line Lexicographic order topology ... more details
Unreferenced stub auto yes date December 2009 Orphan date December 2009 A topology table is used by router s that route traffic in a network. It consists of all routing tables inside the Autonomous system Internet Autonomous System where the router is positioned. Each router using the routing protocol EIGRP then maintains a topology table for each configured network protocol all routes learned, that are leading to a destination are found in the topology table. DEFAULTSORT Topology Table Category Routing Category Network topology Table Compu network stub ... more details
Unreferenced date December 2009 TWCleanup About the study of the World Wide Web links in the mathematical field of topology Link knot theory Link topology is the study of the linked structure of the World Wide Web . See also Link awareness DEFAULTSORT Link Topology Category World Wide Web Web stub ... more details
In topology , a branch of mathematics , an extension topology is a topology structure topology placed ... of extension topology, described in the sections below. Extension topology Let X be a topological space and P a set disjoint from X. Consider in X &cup P the topology whose open sets are of the form ... and Q is a subset of P. For these reasons this topology is called the extension topology of X plus ... topology of X as a subset of X &cup P is the original topology of X, while the subspace topology of P as a subset of X &cup P is the discrete space discrete topology . Being Y a topological space and R a subset of Y, one might ask whether the extension topology of Y R plus R is the same as the original topology of Y, and the answer is in general no. Note the similitude of this extension topology construction and the One point compactification Alexandroff one point compactification ... , where B is a closed set of X. Open extension topology Let X be a topological space and P a set disjoint from X. Consider in X &cup P the topology whose open sets are of the form X &cup Q, where Q is a subset of P, or A, where A is an open set of X. For this reason this topology is called the open extension topology of X plus P, with which one extends to X &cup P the open sets of X. Note that the subspace topology of X as a subset of X &cup P is the original topology of X, while the subspace topology of P as a subset of X &cup P is the discrete space discrete topology . Note that the closed sets of X &cup P are of the form ... space and R a subset of Y, one might ask whether the extension topology of Y R plus R is the same as the original topology of Y, and the answer is in general no. Note that the open extension topology of X &cup P is comparison of topologies smaller than the extension topology of X &cup P. Being Z a set and p a point in Z, one obtains the excluded point topology construction ... more details
In the mathematics mathematical field of functional analysis there are several standard topology topologies ... in the uniform operator topology . If math T n x to Tx math for all x in H , then we say math T n to T math in the strong operator topology . Finally, suppose math T n x to Tx math in the weak topology of H . This means that math F T n x to F T x math for all linear functionals F on H . In this case we say that math T n to T math in the weak operator topology . All of these notions make sense ... are all locally convex, which implies that they are defined by a family of seminorm s. In analysis, a topology ... modes of convergence are, respectively, strong and weak. In topology proper, these terms ... is defined to be the weakest topology on A such that all elements of B are continuous. The norm topology or uniform topology or uniform operator topology is defined by the usual norm x on B H . It is stronger than all the other topologies below. The weak topology weak Banach space topology is B H , B H sup sup , in other words the weakest topology such that all elements of the dual B H sup sup are continuous. It is the weak topology on the Banach space B H . It is stronger than the ultraweak and weak operator topologies. Warning the weak Banach space topology and the weak operator topology and the ultraweak topology are all sometimes called the weak topology, but they are different. The Mackey topology or Arens Mackey topology is the strongest locally convex topology on B H such that the dual is B H sub sub , and is also the uniform convergence topology on B H sub sub , B H compact convex subsets of B H sub sub . It is stronger than all topologies below. The strong sup sup topology or ultrastrong sup sup topology is the weakest topology stronger than the ultrastrong topology .... The strong topology or ultrastrong topology or strongest topology or strongest operator topology ... than all the topologies below other than the strong sup sup topology. Warning in spite ... more details
In functional analysis and related areas of mathematics , the Mackey topology , named after George Mackey , is the finer topology finest topology for a topological vector space which still preserves the continuous dual . In other words the Mackey topology does not make linear functions continuous which were discontinuous in the default topology. The Mackey topology is the opposite of the weak topology , which is the coarser topology coarsest topology on a topological vector space which preserves the continuity of all linear functions in the continuous dual. The Mackey Arens theorem states that all possible dual topology dual topologies are finer than the weak topology and coarser than the Mackey topology. Definition Given a dual pair math X,X math with math X math a topological vector space and math X math its continuous dual the Mackey topology math tau X,X math is a polar topology defined on math X math by using the set of all absolutely convex and weak topology weakly compact sets in math X math . Examples Every metrisable locally convex space math X, tau math with continuous dual math X math carries the Mackey topology, that is math tau tau X, X math , or to put it more succinctly every Mackey space carries the Mackey topology Every Fr chet space math X, tau math carries the Mackey topology and the topology coincides with the strong topology , that is math tau tau X, X beta X, X math See also polar topology weak topology strong topology References springer id M m062080 title Mackey topology author A.I. Shtern cite journal last Mackey first G.W. authorlink George Mackey title On convex topological linear spaces journal Trans. Amer. Math. Soc. volume 60 year 1946 pages 519 537 doi 10.2307 1990352 url http jstor.org stable 1990352 issue 3 publisher Transactions of the American Mathematical Society, Vol. 60, No. 3 cite book last Bourbaki first Nicolas authorlink Nicolas Bourbaki title Topological vector spaces series Elements of mathematics publisher Addison Wesley year ... more details
incomplete date August 2009 In mathematics , general topology or point set topology is the branch of topology ... from other branches of topology in that the topological spaces may be very general, and do not have to be at all similar to manifold s. Definition A topology is a pair X , consisting of a set mathematics ... intersection of open sets is an open set. X and the empty set are open sets. History General topology ... line once known as the topology of point sets , this usage is now obsolete the introduction ... of functional analysis . General topology assumed its present form around 1940. It captures, one might ... topology that basic notions are defined and theorems about them proved. This includes the following open set open and closed set s interior topology interior and closure topology closure neighbourhood topology neighbourhood and closeness topology closeness compact space compactness and connected space connectedness continuous function topology continuous function mathematics function s limit of a sequence .... Set theoretic topology examines such questions when they have substantial relations to set theory , as is often the case. Other main branches of topology are algebraic topology , geometric topology , and differential topology . As the name implies, general topology provides the common foundation for these areas. An important variant of general topology is pointless topology , which, rather ... also Glossary of general topology for detailed definitions List of general topology topics for related articles Category of topological spaces References Some standard books on general topology include Bourbaki cite Topologie G n rale cite cite General Topology cite ISBN 0 387 19374 X John L. Kelley cite General Topology cite ISBN 0 387 90125 6 James Munkres cite Topology cite ISBN 0 13 181629 2 Ryszard Engelking cite General Topology cite ISBN 3 88538 006 4 Citation last1 Steen first1 Lynn Arthur ..., Jr. title Counterexamples in Topology origyear 1978 publisher Springer Verlag location Berlin, New ... more details
Spacetime topology , the Topological space topological structure of spacetime , is a subject studied ... and the concepts of topology thus become important in analysing local as well as global aspects of spacetime. The study of spacetime topology is especially important in physical cosmology . Types of topology There are two main types of topology for a spacetime math M math Manifold topology As with any manifold, a spacetime possesses a natural manifold topology. Here the open set s are the image of open sets in math mathbb R 4 math . Path or Zeeman topology Definition ref name Bombelli http www.phy.olemiss.edu 7Eluca Topics t top st.html Luca Bombelli website ref The topology math rho math in which a subset math E subset M math is open topology open if for every timelike curve math c math there is a set math O math in the manifold topology such that math E cap c O cap c math . It is the finest topology which induces the same topology as math M math does on timelike curves. Properties Strictly finer topology finer than the manifold topology. It is therefore Hausdorff space Hausdorff , Separable topology separable but not Locally compact space locally compact . A Base topology base for the topology is sets of the form math I p,U cup I p,U cup p math for some point math p in M ... structure Causal structure chronological past and future . Alexandrov topology The Alexandrov topology on spacetime, is the Comparison of topologies coarsest topology such that both math I E math and math I E math are open for all subsets math E subset M math . Here the Base topology base of open set s for the topology are sets of the form math I x cap I y math for some points math ,x,y in M math . This topology coincides with the manifold topology iff the manifold is Causality conditions Strongly causal strongly causal but in general it is coarser. Note, that in mathematics, an Alexandrov topology on a partial order is usually taken to be the coarsest topology in which only the upper sets ... more details
Topology is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation stretching without tearing or gluing these properties are the topological invariants. Topology may also refer to Topology, the collection of open sets used to define a topological space Topology journal Topology journal , a mathematical journal, with an emphasis on subject areas related to topology and geometry Topology, a term used in architecture to describe spatial effects which cannot be described by topography, i.e., social, economical, spatial or phenomenological interactions Topology, a term used in cell biology to describe the Membrane topology specific orientation of transmembrane proteins . Topology electronics , a configuration of electronic components. Network topology , a term used to describe configurations of computer networks Topology musical ensemble , an Australian post classical quintet Geospatial topology is the study or science of places with applications in earth science , geography , human geography , and geomorphology . In geographic information system s and their data structures, the terms Geospatial topologytopology and planar enforcement are used to indicate that the border line between two neighboring areas and the border point between two connecting lines is stored only once. Thus, any rounding errors might move the border, but will not lead to gaps or overlaps between the areas. Also in cartography, a topological map is a much simplified map that preserves the mathematical topology while sacrificing scale and shape Topology is often confused with the geographic meaning of topography originally the study of places . The confusion may be a factor in topographies having become confused with terrain or relief , such that they are essentially synonymous. In phylogenetics , the branching pattern of a phylogenetic tree. Topologilinux , a Linux distribution disambig de Topologie es Topolog a desambiguaci n fa fr Topologie ... more details
The topology of an electronic circuit is the form taken by the Network analysis electrical circuits network ... are regarded as being the same topology. Strictly speaking, replacing a component with one of an entirely different type is still the same topology. In some contexts, however, these can loosely ... and low pass topologies even though the network topology is identical. A more correct term for these classes ... value is Prototype filter prototype network . Mathematical topology Electronic network topology is related to topology mathematical topology , in particular, for networks which contain only two terminal devices, circuit topology can be viewed as an application of graph theory . In a Network analysis ... are the edge graph theory edges of graph theory. Two networks of this kind have the same topology ... branches in both circuits. Topology names Many topology names relate to their appearance ... topology equivalents.svg thumb 700px center All these topologies are identical. Series topology is a general ... is a common name for the topology in filter design. For a network with three branches there are four ... with three branches Note that the parallel series topology is another representation of the Delta topology discussed below. Series and parallel topologies can continue to be constructed with greater ... rules. The Y topology is also called star topology. However, star topology may also refer to the more ... main Electronic filter topology Image Filter topologies.svg 425px left The topologies shown opposite ... section is identical topology to the potential divider topology. The T section is identical topology to the Y topology. The section is identical topology to the topology. All these topologies can be viewed as a short section of a ladder topology . Longer sections would normally be described as ladder topology. These kinds of circuits are commonly analysed and characterised in terms of a two port network . clear Bridge topology Main Bridge circuit Image Depictions of bridge topology.svg 750px ... more details
Unreferenced date December 2006 orphan date November 2009 In topology , a hereditarily unicoherent , arcwise connected Path connectedness arcwise connected continuum topology continuum is called a dendroid. A continuum X is called hereditarily unicoherent if every subcontinuum of X is unicoherent . A locally connected dendroid is called a dendrite mathematics dendrite . DEFAULTSORT Dendroid Topology Category Continuum theory Topology stub ... more details
Image with unknown copyright status removed Image line network.gif frame Image showing line network layout A linear bus topology is a network topology consisting of a main run of cable with a terminator at each end. All nodes file server, workstations, and peripherals are connected to the linear cable. Ethernet and LocalTalk networks use a linear bus topology. Advantages of a linear bus topology Easy to connect a computer or peripheral to a linear bus. Requires less cable length than a star topology . Disadvantages of a linear bus topology Entire network shuts down if there is a break in the main cable. Terminators are required at both ends of the backbone cable. Difficult to identify the problem if the entire network shuts down. Not meant to be used as a stand alone solution in a large building. External links http fcit.usf.edu network chap5 chap5.htm Category Network topology compu network stub id Topologi linier ... more details
In mathematics and theoretical computer science the Lawson topology , named after J. D. Lawson, is a topology on partially ordered set s used in the study of domain theory . The lower topology on a poset P is generated by the subbasis consisting of all complements of principal filter mathematics filters on P . The Lawson topology on P is the smallest common refinement of the lower topology and the Scott topology on P . Properties If P is a complete upper semilattice , the Lawson topology on P is always a complete T sub 1 sub topology. See also Scott continuity References G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott 2003 , Continuous Lattices and Domains , Encyclopedia of Mathematics and its Applications, Cambridge University Press. ISBN 0 521 80338 1 External links http www.entcs.org files mfps19 83011.pdf How Do Domains Model Topologies? , Pawel Waszkiewicz, Electronic Notes in Theoretical Computer Science 83 2004 topology stub Category Domain theory Category General topology ... more details
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