https://topospaces.subwiki.org/w/index.php?action=history&feed=atom&title=Protometrizable_space 2026-07-31T03:02:38Z Revision history for this page on the wiki MediaWiki 1.41.2 https://topospaces.subwiki.org/w/index.php?title=Protometrizable_space&diff=2895&oldid=prev 2009-10-25T00:07:29Z

<p>Created page with &#039;{{topospace property}} ==Definition== {{fillin}} ==Relation with other properties== ===Stronger properties=== {| class=&quot;wikitable&quot; border=&quot;1&quot; ! property !! quick description…&#039;</p> <p><b>New page</b></p><div>{{topospace property}}<br /> <br /> ==Definition==<br /> <br /> {{fillin}}<br /> <br /> ==Relation with other properties==<br /> <br /> ===Stronger properties===<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;1&quot;<br /> ! property !! quick description !! proof of implication !! proof of strictness (reverse implication failure) !! intermediate notions <br /> |-<br /> | [[Weaker than::Metrizable space]] || underlying topology of a [[metric space]] || [[metrizable implies protometrizable]] || [[protometrizable not implies metrizable]] || {{intermediate notions short|protometrizable space|metrizable space}}<br /> |-<br /> | [[Weaker than::Manifold]] || || || ||<br /> |-<br /> | [[Weaker than::Closed sub-Euclidean space]] || || || ||<br /> |}<br /> <br /> ===Weaker properties===<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;1&quot;<br /> ! property !! quick description !! proof of implication !! proof of strictness (reverse implication failure) !! intermediate notions <br /> |-<br /> | [[Stronger than::Elastic space]] || || || || <br /> |-<br /> | [[Stronger than::Monotonically normal space]] || || || || {{intermediate notions short|monotonically normal space|protometrizable space}}<br /> |-<br /> | [[Stronger than::Hereditarily normal space]] || || || ||{{intermediate notions short|hereditarily normal space|protometrizable space}}<br /> |-<br /> | [[Stronger than::Normal space]] || || || || {{intermediate notions short|normal space|protometrizable space}}<br /> |-<br /> | [[Stronger than::Collectionwise normal space]] || || || || {{intermediate notions short|collectionwise normal space|protometrizable space}}<br /> |-<br /> | [[Stronger than::Hereditarily collectionwise normal space]] || || || || {{intermediate notions short|hereditarily collectionwise normal space|protometrizable space}}<br /> |}</div>

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