topological space

Noun

 * 1)  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);  the set X.
 * 2) * 2011, Jonathan A. Barmak, Algebraic Topology of Finite Topological Spaces and Applications, Springer, 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.
 * 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.

Usage notes

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

Translations

 * Afrikaans: topologiese ruimte
 * Chinese:
 * Mandarin:
 * Danish: topologisk rum
 * Finnish:
 * French:
 * Galician: espazo tipolóxico
 * German: topologischer Raum
 * Greek: τοπολογικός χώρος
 * Hebrew:
 * Icelandic: grannrúm
 * Italian: spazio topologico
 * Japanese:
 * Portuguese: espaço topológico
 * Romanian: spațiu topologic
 * Russian: топологи́ческое простра́нство
 * Spanish: espacio topológico
 * Swedish:


 * Chinese:
 * Mandarin:
 * Danish: topologisk rum
 * Finnish:
 * Galician: espazo topolóxico
 * Greek: τοπολογικός χώρος
 * Italian: spazio topologico
 * Swedish:


 * Czech:
 * French:
 * Serbo-Croatian: