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First-countable space

In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space X {\displaystyle X} is said to be first-countable if each point has a countable neighbourhood basis (local base). That is, for each point x {\displaystyle x} in X {\displaystyle X} there exists a…

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First-countable space

Nodes46
Edges45
Triples9
Avg. degree1.96
Density0.043478
Components1

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First-countable space

Top relations

related to Properties · 7
First-countable space → Also, Every, Fréchet-Urysohn, However, In, One, This
is a · 2
First-countable space → Fréchet-Urysohn space and thus also a sequential space, topological space satisfying the

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Important terminology

space displaystyle first-countable point right every sequence countable left topology mathematics neighbourhood uncountable omega first base spaces subset local basis

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
First-countable spaceis atopological space satisfying the0.90text
First-countable spaceis aFréchet-Urysohn space and thus also a sequential space0.90text
First-countable spacerelated to PropertiesOne0.60section
First-countable spacerelated to PropertiesIn0.60section
First-countable spacerelated to PropertiesFréchet-Urysohn0.60section
First-countable spacerelated to PropertiesThis0.60section
First-countable spacerelated to PropertiesAlso0.60section
First-countable spacerelated to PropertiesHowever0.60section
First-countable spacerelated to PropertiesEvery0.60section

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    Min side: 3
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