List questions from quotient-spaces

Published on 29 Mar 2026 - 20:27

199

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Quick question about $\mathbb{R} / \mathbb{Z}$ being homeomorphic to $S^1$

Published on 25 Oct 2022 - 9:39

145

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Prove that if $g\circ f$ is a quotient map then $g$ is a quotient map.

Published on 25 Oct 2022 - 17:14

183

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Inverse of projection map is continuous

Published on 27 Oct 2022 - 18:19

86

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Why can the quotient topology not be generated by images of the projection map?

Published on 27 Oct 2022 - 19:24

72

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$\mathbb{R}^2 / \mathbb{R} (1,1)$ equipped with quotient topology

Published on 27 Oct 2022 - 20:58

54

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For each Hausdorff space, a completely regular quotient space. Problem from Dugundji's Topology [mistake on the problem].

Published on 29 Mar 2026 - 20:23

94

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About "incidence" of cosets in homogeneous Riemannian manifolds and their distance

Published on 26 Mar 2026 - 13:52

128

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Probability Theory by Klenke theorem 15.9. That a finite measure is characterized by its characteristic function.

Published on 01 Apr 2026 - 21:31

42

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Doubt in the DoCarmo example 4.8

Published on 02 Nov 2022 - 11:58

140

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Topology of reals quotient by integers AND irrationals is indiscrete?

Published on 05 Nov 2022 - 22:36

180

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Proving that $ X$ is homeomorphic to $ Y / A $

Published on 08 Nov 2022 - 13:02

151

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The homeomorphism between $[0,1]\times[0,1]/\sim_{1}$ and $S^{1}\times[0,1]/\sim_{2}$

Published on 25 Mar 2026 - 22:04

39

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Quotient spaces-vector spaces

Published on 27 Mar 2026 - 22:51

105

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Constructing a homeomorphism $S^1\times S^1/S^1\vee S^1\to S^2$

Published on 10 Nov 2022 - 0:35

List Question

A quotient space of an interval

Quick question about $\mathbb{R} / \mathbb{Z}$ being homeomorphic to $S^1$

Prove that if $g\circ f$ is a quotient map then $g$ is a quotient map.

Inverse of projection map is continuous

Why can the quotient topology not be generated by images of the projection map?

$\mathbb{R}^2 / \mathbb{R} (1,1)$ equipped with quotient topology

For each Hausdorff space, a completely regular quotient space. Problem from Dugundji's Topology [mistake on the problem].

About "incidence" of cosets in homogeneous Riemannian manifolds and their distance

Probability Theory by Klenke theorem 15.9. That a finite measure is characterized by its characteristic function.

Doubt in the DoCarmo example 4.8

Topology of reals quotient by integers AND irrationals is indiscrete?

Proving that $ X$ is homeomorphic to $ Y / A $

The homeomorphism between $[0,1]\times[0,1]/\sim_{1}$ and $S^{1}\times[0,1]/\sim_{2}$

Quotient spaces-vector spaces

Constructing a homeomorphism $S^1\times S^1/S^1\vee S^1\to S^2$

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