What is topological space?

  • (noun): (mathematics) any set of points that satisfy a set of postulates of some kind.
    Example: "Assume that the topological space is finite dimensional"
    Synonyms: mathematical space

Topological Space

Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The branch of mathematics that studies topological spaces in their own right is called topology.

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Some articles on topological space:

Cardinal Functions in Topology
... used in topology as a tool for describing various topological properties ... the definitions, etc.) Perhaps the simplest cardinal invariants of a topological space X are its cardinality and the cardinality of its topology, denoted respectively by
Topological Space - Specializations and Generalizations
... The following spaces and algebras are either more specialized or more general than the topological spaces discussed above ... Proximity spaces provide a notion of closeness of two sets ... Metric spaces embody a metric, a precise notion of distance between points ...
Collectionwise Normal Space
... In mathematics, a topological space is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of there exists a pairwise disjoint family of ... Many authors assume that is also a T1 space as part of the definition, i ... A collectionwise normal T1 space is a collectionwise Hausdorff space ...

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