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Separable space

In mathematics, a topological space is called separable if it contains a countable dense subset; that is, there exists a sequence ( x n ) n = 1 ∞ {\displaystyle (x_{n})_{n=1}^{\infty }} of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

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Explore the main themes, entities and connections around Separable space. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Overview

First examples

Separability versus second countability

Cardinality

Constructive mathematics

Further examples

Properties

Advanced semantic analysis

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Map overview Semantic statistics

Separable space

Nodes78
Edges77
Triples46
Avg. degree1.97
Density0.025641
Components1

How this topic connects Entity context

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Separable space

Top relations

related to Properties · 14
Separable space → Also, For, From, Hausdorff, If, In, Moore, Only, Sierpiński, Sorgenfrey, Th, The, This, Willard
related to Separable spaces · 14
Separable space → An, Any, Banach, Euclidean, Every, Hilbert, It, Mazur, Sorgenfrey, The, The Banach, The Lebesgue, Together, Weierstrass
related to Embedding separable metric spaces · 9
Separable space → Banach, Every, For, Fréchet, Heinonen, Hilbert, Stefan Banach, This, Urysohn
related to Constructive mathematics · 4
Separable space → Banach, Hahn, Separability, Such
related to First examples · 4
Separable space → An, Any, Euclidean, Similarly
is a · 1
Separable space → real line

Important terminology Word statistics

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Important terminology

space separable displaystyle countable subset cardinality every metric dense spaces second hausdorff functions continuous topological subspace set topology real product

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Separable spaceis areal line0.90text
Separable spacerelated to Constructive mathematicsSeparability0.60section
Separable spacerelated to Constructive mathematicsSuch0.60section
Separable spacerelated to Constructive mathematicsHahn0.60section
Separable spacerelated to Constructive mathematicsBanach0.60section
Separable spacerelated to Embedding separable metric spacesEvery0.60section
Separable spacerelated to Embedding separable metric spacesHilbert0.60section
Separable spacerelated to Embedding separable metric spacesThis0.60section
Separable spacerelated to Embedding separable metric spacesUrysohn0.60section
Separable spacerelated to Embedding separable metric spacesBanach0.60section
Separable spacerelated to Embedding separable metric spacesFréchet0.60section
Separable spacerelated to Embedding separable metric spacesHeinonen0.60section

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    Min side: 3
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