Topology
one surface and one edge such shapes are an object of study in topology. Topology Greek language ... that are preserved under continuous deformations. Topology grew out of geometry , but unlike ..
Strong topology (polar topology)
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 ..
Weak topology (polar topology)
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 ..
Uniform topology
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 ..
Strong topology
In mathematics , a strong topology is a topology which is stronger than some other default topology. This term ... topology on the disjoint union topology disjoint union the topology arising from a normed vector ..
Ultraweak topology
In functional analysis , a branch of mathematics , the ultraweak topology , also called the weak topology , or weak operator topology or &sigma weak topology , on the set B H of bounded operator s on a Hilbert ..
Natural topology
In any domain of mathematics , a space has a natural topology if there is a topology on the space which ... means little more than the assertion that the topology in question arises naturally or canonically ..
Dual topology
In functional analysis and related areas of mathematics a dual topology is a locally convex topology ... are trivially a dual pair and the locally convex topology is a dual topology. Several topological ..
Ultrastrong topology
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 ..
Counterexamples in Topology
Infobox Book name Counterexamples in Topology image image caption author Lynn Steen Lynn Arthur Steen ... 244pp. isbn ISBN 048668735X br Dover edition Counterexamples in Topology 1970, 2nd ed. 1978 is a book ..
Finite topology
It is possible for a topology to be finite in the sense that there are only finitely many open sets. This is an extreme ... topology is also encountered in a completely different sense in the study of surfaces . A surface ..
Spacetime topology
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 ..
Extension topology
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 ..
Mackey topology
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 ..
General topology
In mathematics , general topology or point set topology is the branch of topology which studies properties of topological space s and structures defined on them. It is distinct from other branches of topology ..
Operator topology
In mathematics , the requirements of functional analysis mean there are several standard topology topologies ... over the unit ball in H , we say that math T n to T math in the uniform operator topology . If math ..
Geometric topology
otheruses In mathematics , geometric topology is the study of manifold s and their embedding s. Low dimensional topology , concerning questions of dimensions up to four, is a part of geometric topology ..
Computational topology
Algorithmic topology , or computational topology , is a subfield of topology with an overlap with areas ... concern of algorithmic topology, as its name suggests, is to develop efficient algorithm s for solving ..
Topology table
A topology table is used by router s that route traffic in a network. It consists of all routing tables ... using the routing protocol EIGRP then maintains a topology table for each configured network protocol ..
Topology (electronics)
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 ..
DNA topology
DNA topology is the focus of an interdiscipline between molecular biology and mathematics and as a term refers to DNA supercoiling , knotting and catenation . More simply put, DNA topology studies the shape ..
Logical topology
Logical Topology also referred to as Signal Topology is a network computing term used to describe the arrangement ..., is called the Network topology physical topology . Logical topologies are bound to network ..
Cocountable topology
The cocountable topology or countable complement topology on any set X consists of the empty set and all ... topology is Lindelöf space Lindelöf , since every open set only omits countably many points ..
Poset topology
In mathematics , the poset topology associated with a partially ordered set S or poset for short is the Alexandrov topology open sets are upper set s on the poset of finite chains of S, ordered by inclusion ..
Geometry and topology
for the mathematical journal Geometry and Topology In mathematics , geometry and topology is an umbrella term for geometry and topology , as the line between these two is often blurred, most visibly in Riemannian ..
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