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For any property p of topological spaces, p implies locally p.

topospaces.subwiki.org. Locally operator

Locally path-connected space … This property is obtained by applying the locally operator to the property: path-connected space

topospaces.subwiki.org. Locally path-connected space

This space is obviously path-connected, but it is not locally path-connected

math.stackexchange.com

This seems like a contradiction.

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    What is the question?2012-08-04
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    @Keenan Kidwell: Is there a contradiction, or I can't see something? If so, where does the contradiction lie (on what page)?2012-08-05

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