Definitions for topological space
topo·log·i·cal space

Princeton's WordNetRate this definition:0.0 / 0 votes

1. mathematical space, topological spacenoun

   (mathematics) any set of points that satisfy a set of postulates of some kind

   "assume that the topological space is finite dimensional"

WiktionaryRate this definition:0.0 / 0 votes

1. topological spacenoun

   A set, together with a collection of its subsets that form a topology on the set.

2. topological spacenoun

   The set itself.

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1. topological space

   A topological space is a set equipped with a structure, called a topology, that allows the definition of concepts such as continuity, convergence, and closeness. This structure is a collection of subsets, known as open sets, that satisfy the following properties: 1. The entire set and the empty set are both in the collection. 2. The intersection of a finite number of sets in the collection is also in the collection. 3. The union of any number of sets in the collection is also in the collection. In other words, a topological space is a pair (X, τ), where X is a set and τ is a collection of subsets of X (which are called 'open sets') such that: 1. The empty set and X itself are in τ. 2. Any union of members of τ is also a member of τ. 3. The intersection of any finite number of members of τ is also a member of τ.

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1. Topological space

   In topology and related branches of mathematics, a topological space is a set of points, along with a set of neighbourhoods for each point, that satisfy a set of axioms relating points and neighbourhoods. The definition of a topological space relies only upon set theory and is the most general notion of a mathematical "space" that allows for the definition of concepts such as continuity, connectedness, and convergence. Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints. Being so general, topological spaces are a central unifying notion and appear in virtually every branch of modern mathematics. The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.

Matched Categories

1. • Set
   • Space

How to pronounce topological space?

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How to say topological space in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of topological space in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of topological space in Pythagorean Numerology is: 7

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=topological space
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Topological_Space
3. ^ ChatGPT
   https://chat.openai.com
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=topological space