List questions from connectedness

Published on 13 Mar 2014 - 23:10

490

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Let C be a circle. Show that the only subset of C homeomorphic to a circle is C itself

Published on 15 Mar 2014 - 2:44

114

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Show that there exists a path of class $C^1$ between $x$ and $y$

Published on 16 Mar 2014 - 10:22

8.6k

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A contractible space is path connected.

Published on 17 Mar 2014 - 17:27

1.8k

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Find a subset of $\mathbb{R}^2$ that is path connected but is locally connected at none of its points.

Published on 18 Mar 2014 - 12:37

294

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Connected set on topology - Contradiction

Published on 18 Mar 2014 - 23:33

349

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Is there any point-set definition of simple connectedness?

Published on 20 Mar 2014 - 6:37

88

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Path-Connectedness of Union

Published on 20 Mar 2014 - 22:13

302

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Prove $Y$ is connected

Published on 21 Mar 2014 - 7:06

389

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Theorem 23.5 from topology by James Munkres

Published on 22 Mar 2014 - 11:38

467

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Homeomorphism between topological space and product space

Published on 25 Mar 2026 - 17:43

2.3k

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Homotopy equivalence induces bijection between path components

Published on 25 Mar 2014 - 4:42

685

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Question about the definition of homology

Published on 26 Mar 2014 - 21:10

1.5k

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Are there path-connected but not polygonal-connected sets?

Published on 27 Mar 2014 - 6:15

3.4k

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Degree sequence of connected graphs

Published on 30 Mar 2014 - 9:57

List Question

Prove that the manifold $SO(n)$ is connected

Let C be a circle. Show that the only subset of C homeomorphic to a circle is C itself

Show that there exists a path of class $C^1$ between $x$ and $y$

A contractible space is path connected.

Find a subset of $\mathbb{R}^2$ that is path connected but is locally connected at none of its points.

Connected set on topology - Contradiction

Is there any point-set definition of simple connectedness?

Path-Connectedness of Union

Prove $Y$ is connected

Theorem 23.5 from topology by James Munkres

Homeomorphism between topological space and product space

Homotopy equivalence induces bijection between path components

Question about the definition of homology

Are there path-connected but not polygonal-connected sets?

Degree sequence of connected graphs

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