https://topospaces.subwiki.org/w/index.php?action=history&feed=atom&title=Locally_connected_not_implies_locally_path-connected 2026-09-07T16:20:03Z Revision history for this page on the wiki MediaWiki 1.41.2 https://topospaces.subwiki.org/w/index.php?title=Locally_connected_not_implies_locally_path-connected&diff=3009&oldid=prev 2009-12-25T07:34:40Z

<p>Created page with &#039;{{topospace property non-implication| stronger = locally connected space| weaker = locally path-connected space}} ==Statement== It is possible for a [[topological space] to be …&#039;</p> <p><b>New page</b></p><div>{{topospace property non-implication|<br /> stronger = locally connected space|<br /> weaker = locally path-connected space}}<br /> <br /> ==Statement==<br /> <br /> It is possible for a [[topological space] to be a [[locally connected space]] but &#039;&#039;not&#039;&#039; a [[locally path-connected space]].<br /> <br /> ==Definitions used==<br /> <br /> ===Locally connected space===<br /> <br /> {{further|[[locally connected space]]}}<br /> <br /> ===Locally path-connected space===<br /> <br /> {{further|[[locally path-connected space]]}}<br /> <br /> ==Related facts==<br /> <br /> ===Converse===<br /> <br /> [[Locally path-connected implies locally connected]]<br /> <br /> ===Other related facts===<br /> <br /> * [[Connected not implies path-connected]]<br /> * [[Connected and locally path-connected implies path-connected]]<br /> * [[Path-connected implies connected]]<br /> ==Proof==<br /> <br /> {{fillin}}</div>

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