Collectionwise normal and Moore implies metrizable: Difference between revisions
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The statement has the following equivalent forms: | The statement has the following equivalent forms: | ||
# If a [[topological space]] is both [[collectionwise normal space|collectionwise normal]] and a [[Moore space]], then it is a [[metrizable space]]. | # If a [[topological space]] is both [[uses property satisfaction of::collectionwise normal space|collectionwise normal]] and a [[uses property satisfactin of::Moore space]], then it is a [[proves property satisfaction of::metrizable space]]. | ||
# If a [[topological space]] is both [[collectionwise normal space|collectionwise normal]] and a [[developable space]], then it is a [[metrizable space]]. | # If a [[topological space]] is both [[collectionwise normal space|collectionwise normal]] and a [[uses property satisfaction of::developable space]], then it is a [[metrizable space]]. | ||
Revision as of 02:45, 27 January 2012
Template:Metrizability theorem
History
This statement was proved by Moore.
Statement
The statement has the following equivalent forms:
- If a topological space is both collectionwise normal and a Moore space, then it is a metrizable space.
- If a topological space is both collectionwise normal and a developable space, then it is a metrizable space.