(Q926996)

English

first-countable space

topological space in which every point admits a countable neighborhood basis

first axiom of countability

In more languages

edit

Statements

subclass of

topological space

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defining formula

\forall x\in X\exists {\mathcal {B}}\subset {\mathcal {N}}_{x}\colon |{\mathcal {B}}|\leq \aleph _{0}\land \forall N\in {\mathcal {N}}_{x}\exists B\in {\mathcal {B}}\colon B\subset N

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in defining formula

X

symbol represents

first-countable space

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{\mathcal {N}}_{x}

symbol represents

neighborhood system

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\aleph _{0}

symbol represents

aleph null

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N

symbol represents

neighborhood

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\land

symbol represents

logical conjunction

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

1 reference

Encyclopedia of Mathematics article ID

First_axiom_of_countability

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1 reference

28 October 2013

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Metamath statement ID

df-1stc

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Microsoft Academic ID

118630013

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nLab ID

first-countable space

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PlanetMath ID

FirstCountable

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FirstAxiomOfCountability

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ProofWiki ID

Definition:First-Countable_Space

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Sitelinks

Wikipedia(12 entries)

cawiki Primer axioma de numerabilitat
enwiki First-countable space
eswiki Primer axioma de numerabilidad
frwiki Espace à bases dénombrables de voisinages
glwiki Primeiro axioma de numerabilidade
itwiki Spazio primo-numerabile
jawiki 第一可算的空間
kowiki 제1 가산 공간
ruwiki Первая аксиома счётности
ukwiki Перша аксіома зліченності
viwiki Không gian đếm được bậc nhất
zhwiki 第一可數空間

(Q926996)

first-countable space

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Wikipedia(12 entries)

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