Encyclopedia results for Topological space

1. Topological space
   For a general, non technical overview of the subject Topology Image Topological space examples.svg frame ... topological spaces in their own right is called topology . Definition A topological space is a set ..
   
   
   
2. Topological vector space
   Image Topological vector space illust1.svg right thumb The addition operation is continuous at 0 if and only ... addition V     V is contained in U . In mathematics , a topological vector space is one of the basic ..
   
   
   
3. Noetherian topological space
   In mathematics , a Noetherian topological space is a topological space in which closed subsets satisfy ... stronger statement that every subset is compact. Definition A topological space math X math ..
   
   
   
4. Finite topological space
   In mathematics , a finite topological space is a topological space for which the underlying set mathematics point set is finite set finite . That is, it is a topological space for which there are only ..
   
   
   
5. Localization of a topological space
   In mathematics, well behaved topological spaces can be localized at primes, in a similar way to the localization ... of making topology, more precisely algebraic topology , more geometric. Localization of a space ..
   
   
   
6. Bounded set (topological vector space)
   In functional analysis and related areas of mathematics , a set in a topological vector space is called .... Definition Given a topological vector space X ,&tau over a field mathematics field F , S is called ..
   
   
   
7. Locally convex topological vector space
   convex spaces are examples of topological vector space s TVS which generalise normed space s. They can be defined as topological space topological vector spaces whose topology is base topology ..
   
   
   
8. Topological module
   A topological vector space is a topological module over a topological field . An abelian group ...Expand date July 2007 In mathematics , a topological module is a module algebra module over a topological ..
   
   
   
9. Topological algebra
   In mathematics , a topological algebra A is a topological vector space with a continuous multiplication ... by David van Dantzig it appears in the title of his Thesis doctoral dissertation 1931 . Category Topological ..
   
   
   
10. Topological manifold
    In mathematics , a topological manifold is a Hausdorff space Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class ..
    
    
    
11. Topological group
    In mathematics , a topological group is a group mathematics group G together with a topological space ..., G × G is viewed as a topological space by using the product topology . Although we do not do ..
    
    
    
12. Topological semigroup
    In mathematics , a topological semigroup is a semigroup which is simultaneously a topological space , and whose ... continuous addition. ref A topological group is a topological semigroup. TODO Cite a more ..
    
    
    
13. Topological game
    A topological game is an infinite positional game of perfect information played between two players on a topological space . Players choose objects with topological properties such as points, open sets ..
    
    
    
14. Topological ring
    In mathematics , a topological ring is a ring algebra ring R which is also a topological space such that both ... s on some normed vector space all Banach algebra s are topological rings. The rational number rational ..
    
    
    
15. Topological property
    of a topological space which is invariant mathematics invariant under homeomorphism s. That is, a property of spaces is a topological property if whenever a space X possesses that property every ..
    
    
    
16. Topological entropy
    . Definition A topological dynamical system consists of a Hausdorff topological space X usually assumed .... Definition of Adler, Konheim, and McAndrew Let X be a compact Hausdorff topological space. For any ..
    
    
    
17. Topological indistinguishability
    In topology , two points of a topological space X are topologically indistinguishable if they have exactly ... space T sub 0 sub space is a topological space in which every pair of distinct points is topologically ..
    
    
    
18. Topological conjugacy
    conjugate. Definition Let math X math and math Y math be topological space s, and let math ... a homeomorphism that will conjugate the one into the other. Topological conjugacy is important in the study ..
    
    
    
19. Topological sorting
    In graph theory , a topological sort or topological ordering of a directed acyclic graph DAG is a linear ... DAG has one or more topological sorts. More formally, define the partial order relation R over ..
    
    
    
20. Topological map
    Image Unintentional Humor, Way In, No Entry.jpg 250px right thumb Topological tube map of the London Underground In cartography and geology , a topological map refers to a map that has been topology simplified ..
    
    
    
21. Topological index
    In chemical graph theory and in mathematical chemistry , a topological index is any of several numerical ... Handbook of Molecular Descriptors , Wiley VCH , ISBN 3527299130 ref The Hosoya index is the first topological ..
    
    
    
22. Topological defect
    . In mathematics and physics , a topological soliton or a topological defect is a solution of a system ... are then topologically distinct , and are classified by their homotopy class . Topological ..
    
    
    
23. Topological order
    Otheruses4 quantum physics the graph theoretical concept topological sort In physics , topological order ... and Long range order long range correlations . However, topological orders can be described ..
    
    
    
24. Topological censorship
    The topological censorship theorem states that general relativity does not allow an observer to probe the topology of spacetime any topological structure collapses too quickly to allow light to traverse ..
    
    
    
25. Topological derivative
    Expand date May 2007 expert subject mathematics In the field of shape optimization , a topological derivative ... al. http www.cmap.polytechnique.fr jouve papers toplev.pdf Structural optimization using topological ..