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Topic: Locally Connected
Replies: 1   Last Post: May 23, 2014 11:24 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Locally Connected
Posted: May 19, 2014 10:23 AM
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Is there a locally connected, metrizable
space that's not locally path connected?

Compact, connected, locally connected, metrizable spaces
(Peano spaces) are path connected, in fact arc connected.

Is there a connected, locally connected,
metrizable space that's not path connected?

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