Encyclopedia results for topology

1. Topology
   one surface and one edge such shapes are an object of study in topology. Topology Greek language ... . Topology begins with a consideration of the nature of space, investigating both its fine structure ..
   
   
   
2. 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 ..
   
   
   
3. 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 ..
   
   
   
4. 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 ..
   
   
   
5. 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 ..
   
   
   
6. Upper topology
   In mathematics , the upper topology is the topological space topology defined on a preorder preordered set in which the open set s are the up set s. The upper topology on the set math X mathbb R math is defined ..
   
   
   
7. 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 ..
   
   
   
8. 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 ..
   
   
   
9. 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 ..
   
   
   
10. 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 ..
    
    
    
11. Initial topology
    In general topology and related areas of mathematics , the initial topology projective topology or weak topology on a set math X math , with respect to a family of functions on math X math , is the coarsest ..
    
    
    
12. 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 ..
    
    
    
13. Weak topology
    dablink This article discusses the weak topology on a normed vector space. For the weak topology induced by a family of maps see initial topology . For the weak topology generated by a cover of a space ..
    
    
    
14. 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 ..
    
    
    
15. Product topology
    In topology and related areas of mathematics , a product space is the cartesian product of a family of topological space s equipped with a natural topology called the product topology . This topology differs ..
    
    
    
16. Final topology
    In general topology and related areas of mathematics , the final topology inductive topology or strong topology on a set math X math , with respect to a family of functions into math X math , is the finest ..
    
    
    
17. Extension topology
    In topology , a branch of mathematics , an extension topology is a topology structure topology placed ... topology, described in the sections below. Extension topology Let X be a topological space and P a set ..
    
    
    
18. Order topology
    In mathematics , an order topology is a certain topology that can be defined on any totally ordered set . It is a natural generalization of the topology of the real numbers to arbitrary totally ordered ..
    
    
    
19. 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 ..
    
    
    
20. Box topology
    In topology , the cartesian product of topological space s can be given several different topologies. The canonical one is the product topology , because it fits rather nicely with the Category theory ..
    
    
    
21. 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 ..
    
    
    
22. 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 ..
    
    
    
23. Topology (electronics)
    The topology of an electronic circuit is the basic configuration of the circuit without regard to specific component values or ratings. Schematic diagrams illustrating circuit topology often show only ..
    
    
    
24. 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 ..
    
    
    
25. Coherent topology
    In topology , a coherent topology is one that is uniquely determined by a family of subspaces. Loosely ... family family of subspace topology subspace s of X typically C will be a cover topology cover of X ..