## 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:

... 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 ...

... 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**...

### Famous quotes containing the word space:

“In bourgeois society, the French and the industrial revolution transformed the authorization of political *space*. The political revolution put an end to the formalized hierarchy of the ancien regimé.... Concurrently, the industrial revolution subverted the social hierarchy upon which the old political *space* was based. It transformed the experience of society from one of vertical hierarchy to one of horizontal class stratification.”

—Donald M. Lowe, U.S. historian, educator. History of Bourgeois Perception, ch. 4, University of Chicago Press (1982)