(Q1363919)

English

second-countable space

topological space whose topology admits a countable base

completely separable space
second axiom of countability

In more languages

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Statements

subclass of

separable space

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first-countable space

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Lindelöf space

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defining formula

\exists {\mathcal {B}}\subset \operatorname {Open} (X)\colon |{\mathcal {B}}|\leq \aleph _{0}\land \forall U\in \operatorname {Open} (X)\exists B\in {\mathcal {B}}\colon B\subset U

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in defining formula

X

symbol represents

second-countable space

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{\mathcal {B}}

symbol represents

base

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\aleph _{0}

symbol represents

aleph null

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\operatorname {Open} (X)

symbol represents

topology

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U

symbol represents

open set

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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

Second_axiom_of_countability

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1 reference

28 October 2013

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imported from Wikimedia project

Japanese Wikipedia

SecondCountableTopology

reason for deprecated rank

does not exactly match

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Microsoft Academic ID

162362422

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nLab ID

second-countable space

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1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

PlanetMath ID

SecondCountable

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ProofWiki ID

Definition:Second-Countable_Space

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(Q1363919)

second-countable space

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