List questions from locally-connected

Published on 23 Feb 2026 - 1:04

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Locally connected implies disjoint union of open connected sets

Published on 30 Oct 2017 - 18:23

5.5k

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Any example of a connected space that is not locally connected?

Published on 02 Jan 2018 - 20:36

437

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Not locally connected but path connected particular example

Published on 05 Jan 2018 - 19:49

145

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Some Counterexamples on Connectedness

Published on 05 Aug 2020 - 0:19

83

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Maps between Peano spaces

Published on 07 Aug 2020 - 18:51

152

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Characterization of Connected Locally Connected Sets

Published on 15 Aug 2020 - 22:27

83

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Existence of a connected neighborhood does not imply local connectedness

Published on 28 Aug 2020 - 3:16

187

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Closure of topology sine $Y = \lbrace (x,\sin(\frac{1}{x})) : x > 0 \rbrace $

Published on 08 Sep 2020 - 6:07

25

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Possibly differing definitions of local path-connectedness

Published on 18 Sep 2020 - 18:24

374

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$ X = A \cup B $ where $ A $ and $ B $ are closed and $ A \cap B $ is locally connected. Show that $A$ and $B$ are locally connected.

Published on 10 Oct 2020 - 2:44

55

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the boundary of a component $C$ of $A$ is contained in the boundary of $A $.

Published on 10 Oct 2020 - 16:02

93

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$X$ is locally connected and countably compact

Published on 17 Oct 2020 - 3:59

72

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X is connected and locally connected

Published on 17 Oct 2020 - 13:30

105

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$X$ a compact Hausdorff space has the property $ \mathcal{M} $ if, and only if $X$ is locally connected.

Published on 18 Oct 2020 - 14:15

List Question

Characterisation of One Dimensional Peano Continua

Locally connected implies disjoint union of open connected sets

Any example of a connected space that is not locally connected?

Not locally connected but path connected particular example

Some Counterexamples on Connectedness

Maps between Peano spaces

Characterization of Connected Locally Connected Sets

Existence of a connected neighborhood does not imply local connectedness

Closure of topology sine $Y = \lbrace (x,\sin(\frac{1}{x})) : x > 0 \rbrace $

Possibly differing definitions of local path-connectedness

$ X = A \cup B $ where $ A $ and $ B $ are closed and $ A \cap B $ is locally connected. Show that $A$ and $B$ are locally connected.

the boundary of a component $C$ of $A$ is contained in the boundary of $A $.

$X$ is locally connected and countably compact

X is connected and locally connected

$X$ a compact Hausdorff space has the property $ \mathcal{M} $ if, and only if $X$ is locally connected.

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