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topological space

topological space noun: 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);.

Noun

topological space (plural topological spaces)

  1. (formal) 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);
    • In order to obtain "intuitive insight" into special classes of topological spaces we can proceed in several ways, only a few of which will be pursued in this chapter. For instance, we can seek to describe important topological spaces by means of enough of their properties to completely characterize...1964, H. J. Kowalsky, translated by Jay E. Strum, Topological Spaces, Academic Press, page 165
    • 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.2011, Jonathan A. Barmak, Algebraic Topology of Finite Topological Spaces and Applications, Springer, Lecture Notes in Mathematics 2032, page xi
  2. (broadly, formal) the set X.

topological space meaning in Tamil

topological space in Tamil

இடத்தியலளிப்புக்கணம்

Examples of topological space in a sentence

  • In order to obtain "intuitive insight" into special classes of topological spaces we can proceed in several ways, only a few of which will be pursued in this chapter.1964, H. J. Kowalsky, translated by Jay E. Strum, Topological Spaces, Academic Press, page 165:
  • If (X,#92;tau) is a topological space, then a cover #92;mathcalB is open if each B#92;in#92;mathcalB is an open set.2013, D. J. H. Garling, A Course in Mathematical Analysis: Volume 2, Cambridge University Press, page 431:

Forms of topological space

pluraltopological spaces

Questions about topological space

What does topological space mean?
Topological space means 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);.
What is topological space in Tamil?
Topological space in Tamil is இடத்தியலளிப்புக்கணம். See Topological space meaning in Tamil.
How do you use topological space in a sentence?
In order to obtain "intuitive insight" into special classes of topological spaces we can proceed in several ways, only a few of which will be pursued in this chapter.
What part of speech is topological space?
Topological space is a noun.
What is the plural of topological space?
The plural of topological space is topological spaces.

Words near topological space in the dictionary

  1. topological property
  2. topological soliton
  3. topological solitons
  4. topological sort
  5. topological sorts
  6. topological space
  7. topological spaces
  8. topological vector space
  9. topological vector spaces
  10. topologicality
  11. topologically

Source and license

Adapted from Wiktionary: topological space (page history and authors); topological space (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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