Urysohn is hereditary: Difference between revisions
(Created page with "{{topospace metaproperty satisfaction| property = Urysohn space| metaproperty = subspace-hereditary property of topological spaces}} ==Statement== Any subset of a [[Urysohn ...") |
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| [[completely regular space]] || [[complete regularity is hereditary]] | | [[completely regular space]] || [[complete regularity is hereditary]] | ||
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| [[collectionwise Hausdorff space]] || [[collectionwise Hausdorff is hereditary] | | [[collectionwise Hausdorff space]] || [[collectionwise Hausdorff is hereditary]] | ||
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* [[Normality is weakly hereditary]] | * [[Normality is weakly hereditary]] | ||
* [[Compactness is weakly hereditary]] | * [[Compactness is weakly hereditary]] | ||
* [[Monotone normality is hereditary] | * [[Monotone normality is hereditary]] | ||
===Opposite facts=== | ===Opposite facts=== | ||
* [[Normality is not hereditary] | * [[Normality is not hereditary]] | ||
Latest revision as of 23:14, 27 January 2012
This article gives the statement, and possibly proof, of a topological space property (i.e., Urysohn space) satisfying a topological space metaproperty (i.e., subspace-hereditary property of topological spaces)
View all topological space metaproperty satisfactions | View all topological space metaproperty dissatisfactions
Get more facts about Urysohn space |Get facts that use property satisfaction of Urysohn space | Get facts that use property satisfaction of Urysohn space|Get more facts about subspace-hereditary property of topological spaces
Statement
Any subset of a Urysohn space, endowed with the subspace topology, is also a Urysohn space.
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