Topological space

English

Noun

1. Template:Lb An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);
   Template:Lb the set X.
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   • 2011, Jonathan A. Barmak, Algebraic Topology of Finite Topological Spaces and Applications, Springer, Template:W 2032, page xi,

     Most of the spaces studied in Algebraic Topology, such as CW-complexes or manifolds, are Hausdorff. In contrast, finite topological spaces are rarely Hausdorff. A topological space with finitely many points, each of which is closed, must be discrete.

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Usage notes

• The set $X$ may be called the Template:M.
• The collection $\tau$ may be called the Template:M.
• The topological space $(X,\tau )$ may be described as the underlying set $X$ endowed with the topology $\tau$.

Hypernyms

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Hyponyms

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Meronyms

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Further reading

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• Topological space on Template:W