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Topological space

In mathematics, a topological space is, roughly speaking, a space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point…

History, Examples of topological spaces & Definitions

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Overview

History

Definitions

Comparison of topologies

Continuous functions

Examples of topological spaces

Classification of topological spaces

Bibliography

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Map overview Semantic statistics

Topological space

Nodes162
Edges161
Triples62
Avg. degree1.99
Density0.012346
Components1

How this topic connects Entity context

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Topological space

Top relations

related to Examples of topological spaces · 11
Topological space → Also, Any, Every, Finite, Hausdorff, However, If, Such, The, There, This
see also · 11
Topological space → Compact, Complete Heyting, Function, Generalization, Heyting, In, Mathematical, Semicontinuity, Subset, The, Type
related to Continuous functions · 8
Topological space → Equivalently, From, In, K-theory, The, This, Top, Two
related to Definition via neighbourhoods · 7
Topological space → Any, Felix Hausdorff, If, In, Let, The, This
related to Topology from other topologies · 5
Topological space → Every, For, In, The, This
related to Classification of topological spaces · 4
Topological space → Examples, For, To, Topological
related to External links · 4
Topological space → EMS Press, Encyclopedia, Mathematics, Topological
related to Comparison of topologies · 3
Topological space → Many, The, When
related to Other definitions · 3
Topological space → Another, Kuratowski, There
is a · 2
Topological space → most general type of a mathematical space that allows for the definition of limits, set whose elements are called points

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Important terminology

topology displaystyle set topological space open sets spaces given defined axioms every tau general isbn neighbourhoods called continuous closed neighbourhood

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Topological spaceis aset whose elements are called points0.90text
Topological spaceis amost general type of a mathematical space that allows for the definition of limits0.90text
topological groupsinstance ofThis leads to concepts0.80text
topological ringsinstance ofThis leads to concepts0.80text
topological fieldsinstance ofThis leads to concepts0.80text
topological vector spaces over the latterinstance ofThis leads to concepts0.80text
Topological spacerelated to Classification of topological spacesTopological0.60section
Topological spacerelated to Classification of topological spacesTo0.60section
Topological spacerelated to Classification of topological spacesExamples0.60section
Topological spacerelated to Classification of topological spacesFor0.60section
Topological spacerelated to Comparison of topologiesMany0.60section
Topological spacerelated to Comparison of topologiesWhen0.60section

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    Min side: 3
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