Second-countable space: Difference between revisions
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* [[Separable metrizable space]] | * [[Separable metrizable space]] | ||
* [[Polish space]] | * [[Polish space]] | ||
* [[Sub-Euclidean space]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
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* [[Separable space]] | * [[Separable space]] | ||
* [[First-countable space]] | * [[First-countable space]] | ||
==Metaproperties== | |||
{{subspace-closed}} | |||
Any subspace of a second-countable space is second-countable. | |||
{{countable DP-closed}} | |||
Revision as of 23:41, 10 November 2007
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
A topological space is termed second-countable if it admits a countable basis.
Relation with other properties
Stronger properties
Weaker properties
Metaproperties
Hereditariness
This property of topological spaces is hereditary, or subspace-closed. In other words, any subspace (subset with the subspace topology) of a topological space with this property also has this property.
View other subspace-hereditary properties of topological spaces
Any subspace of a second-countable space is second-countable.