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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);
Definition source: English Wiktionary via Wiktextract
Usage: formal
Topics: mathematics, sciences, topology
Examples
- 2011, Jonathan A. Barmak, Algebraic Topology of Finite Topological Spaces and Applications, Springer, Lecture Notes in Mathematics 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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); (loosely) the set X.
the set X.
Definition source: English Wiktionary via Wiktextract
Usage: broadly, formal
Topics: mathematics, sciences, topology
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
(mathematics) any set of points that satisfy a set of postulates of some kind
Definition source: Princeton WordNet 3.0
Examples
- assume that the topological space is finite dimensional
Meaning relationships
Synonyms: mathematical space
Antonyms: none provided
Broader terms: space, infinite, set
Narrower terms: subspace, null space, manifold, metric space
No etymology was provided for this word.
Across languages
Translations
26 source translations are retained for this English entry.
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Afrikaans:
topologiese ruimte
— ordered pair of a set and its topology
-
Chinese Mandarin:
拓扑空间
(tuòpū kōngjiān)
— ordered pair of a set and its topology
-
Danish:
topologisk rum
— ordered pair of a set and its topology
-
Finnish:
topologinen avaruus
— ordered pair of a set and its topology
-
French:
espace topologique
— ordered pair of a set and its topology
-
Galician:
espazo tipolóxico
— ordered pair of a set and its topology
-
German:
topologischer Raum
— ordered pair of a set and its topology
-
Greek:
τοπολογικός χώρος
(topologikós chóros)
— ordered pair of a set and its topology
-
Hebrew:
מרחב טופולוגי
(mercháv topológi)
— ordered pair of a set and its topology
-
Icelandic:
grannrúm
— ordered pair of a set and its topology
-
Italian:
spazio topologico
— ordered pair of a set and its topology
-
Japanese:
位相空間
(isō kūkan)
— ordered pair of a set and its topology
-
Polish:
przestrzeń topologiczna
— ordered pair of a set and its topology
-
Portuguese:
espaço topológico
— ordered pair of a set and its topology
-
Romanian:
spațiu topologic
— ordered pair of a set and its topology
-
Russian:
топологи́ческое простра́нство
(topologíčeskoje prostránstvo)
— ordered pair of a set and its topology
-
Spanish:
espacio topológico
— ordered pair of a set and its topology
-
Swedish:
topologiskt rum
— ordered pair of a set and its topology
-
Chinese Mandarin:
拓扑空间
(tuòpū kōngjiān)
— set that has a topology
-
Danish:
topologisk rum
— set that has a topology
-
Finnish:
topologinen avaruus
— set that has a topology
-
Galician:
espazo topolóxico
— set that has a topology
-
Greek:
τοπολογικός χώρος
(topologikós chóros)
— set that has a topology
-
Italian:
spazio topologico
— set that has a topology
-
Polish:
przestrzeń topologiczna
— set that has a topology
-
Swedish:
topologiskt rum
— set that has a topology
