Collectionwise normal and Moore implies metrizable - Revision history

Vipul at 02:48, 27 January 2012

2012-01-27T02:48:36Z

← Older revision		Revision as of 02:48, 27 January 2012
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	# 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 [[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 [[uses property satisfaction of::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]].

			Note that the converse is easily seen to be true: [[metrizable implies Moore]] and [[metrizable implies collectionwise normal]]. Thus, the above give necessary and sufficient conditions for a topological space to be metrizable.

Vipul at 02:46, 27 January 2012

2012-01-27T02:46:23Z

← Older revision		Revision as of 02:46, 27 January 2012
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	{{~~metrizability~~ theorem}}		{{metrization theorem}}

	==History==		==History==

Vipul at 02:45, 27 January 2012

2012-01-27T02:45:48Z

← Older revision		Revision as of 02:45, 27 January 2012
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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]].

Vipul: Created page with "{{metrizability theorem}} ==History== This statement was proved by Moore. ==Statement== The statement has the following equivalent forms: # If a topological space is ..."

2012-01-27T02:45:12Z

Created page with "{{metrizability theorem}} ==History== This statement was proved by Moore. ==Statement== The statement has the following equivalent forms: # If a topological space is ..."

New page

{{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 space|collectionwise normal]] and a [[Moore space]], then it is a [[metrizable space]].
# If a [[topological space]] is both [[collectionwise normal space|collectionwise normal]] and a [[developable space]], then it is a [[metrizable space]].