Question

If every open cover of $ X $ admits a finite refinement consisting of connected sets, then $ X $ is locally connected.

score 76 · Answer 1 · 2026-02-23 06:41:05

76

Views

If every open cover of $ X $ admits a finite refinement consisting of connected sets, then $ X $ is locally connected.

Published on 23 Feb 2026 - 6:41

score 38 · Answer 2 · 2026-02-23 06:39:31

38

Views

Show that if $ X $ has the property $ \mathcal{M} $, then $ X $ is locally connected.

Published on 23 Feb 2026 - 6:39

score 49 · Answer 3 · 2026-02-23 06:38:08

49

Views

Metric space locally compact but not uniformly locally connected

Published on 23 Feb 2026 - 6:38

score 233 · Answer 4 · 2026-02-23 06:42:27

233

Views

Local connectedness of topologist's comb

Published on 23 Feb 2026 - 6:42

score 91 · Answer 5 · 2026-02-23 06:35:03

91

Views

Proof Verification : Equivalent Condition for Locally Connected Space

Published on 23 Feb 2026 - 6:35

score 105 · Answer 6 · 2026-02-23 06:42:28

105

Views

X has finitely many connected components, can we get X locally connected?

Published on 23 Feb 2026 - 6:42

score 100 · Answer 7 · 2026-04-09 08:06:54

100

Views

Boundaries in Spaces where Quasicomponents and Components Coincide

Published on 09 Apr 2026 - 8:06

score 126 · Answer 8 · 2026-02-23 06:36:16

126

Views

Is the local connectedness heritable over the connected subspaces?

Published on 23 Feb 2026 - 6:36

score 383 · Answer 9 · 2026-02-23 06:37:53

383

Views

Is every open and connected set in $\mathbb C$ the continuous image of the open unit disk?

Published on 23 Feb 2026 - 6:37

score 111 · Answer 10 · 2026-02-23 06:38:04

111

Views

A sheaf is locally constant iff the etale space is a covering

Published on 23 Feb 2026 - 6:38

score 66 · Answer 11 · 2026-02-23 06:38:44

66

Views

What is this topological property? A form of local connectedness?

Published on 23 Feb 2026 - 6:38

score 75 · Answer 12 · 2026-02-23 06:40:54

75

Views

Types of connectedness for $L_n:=\{(x,\frac{x}{n})\mid0\leq x\leq1\}\subset\mathbb{R}^2$ for $n\in\mathbb{Z}_+$

Published on 23 Feb 2026 - 6:40

score 101 · Answer 13 · 2026-02-23 06:42:03

101

Views

Locally connectedness preserved after removing one point

Published on 23 Feb 2026 - 6:42

score 322 · Answer 14 · 2026-02-23 06:40:28

322

Views

Example of a map of coverings which is not a covering map, if the base space is not locally path-connected

Published on 23 Feb 2026 - 6:40

score 97 · Answer 15 · 2026-02-23 06:41:05

topological properties of $X= \left( \cup_{n=1}^{\infty} \{\frac{1}{n}\} \times [0,1] \right) \cup (\{0\} \times [0,1]) \cup ( [0,1] \times \{0\})$

List Question

If every open cover of $ X $ admits a finite refinement consisting of connected sets, then $ X $ is locally connected.

Show that if $ X $ has the property $ \mathcal{M} $, then $ X $ is locally connected.

Metric space locally compact but not uniformly locally connected

Local connectedness of topologist's comb

Proof Verification : Equivalent Condition for Locally Connected Space

X has finitely many connected components, can we get X locally connected?

Boundaries in Spaces where Quasicomponents and Components Coincide

Is the local connectedness heritable over the connected subspaces?

Is every open and connected set in $\mathbb C$ the continuous image of the open unit disk?

A sheaf is locally constant iff the etale space is a covering

What is this topological property? A form of local connectedness?

Types of connectedness for $L_n:=\{(x,\frac{x}{n})\mid0\leq x\leq1\}\subset\mathbb{R}^2$ for $n\in\mathbb{Z}_+$

Locally connectedness preserved after removing one point

Example of a map of coverings which is not a covering map, if the base space is not locally path-connected

topological properties of $X= \left( \cup_{n=1}^{\infty} \{\frac{1}{n}\} \times [0,1] \right) \cup (\{0\} \times [0,1]) \cup ( [0,1] \times \{0\})$

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