List questions from quotient-spaces

Published on 26 Mar 2026 - 9:30

165

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Injective implies surjective?

Published on 16 Dec 2016 - 15:33

161

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Prove a closed subspace has finite codimension

Published on 17 Dec 2016 - 9:28

86

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Is the limit $C_n[x]/I_n$ exsit when the dimension is infinite？

Published on 17 Dec 2016 - 15:19

67

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Figuring out what $\mathrm{O}(n)/\mathrm{SO}(n)$ is.

Published on 18 Dec 2016 - 3:48

36

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Quotient by squares of finite rank

Published on 18 Dec 2016 - 10:12

745

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Product of two quotient map need not be a quotient map

Published on 26 Dec 2016 - 14:34

90

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Showing that $\varphi: \overline{\mathbb{B}^2} \amalg \overline{\mathbb{B}^2} \to \mathbb{S}^2$ is a quotient map

Published on 29 Dec 2016 - 20:50

477

Views

Prove that $(X\times [0,1])/{\sim'}$ is homeomorphic to $(X/{\sim})\times[0,1].$

Published on 30 Dec 2016 - 16:04

841

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Indiscreet topology on quotient space

Published on 30 Dec 2016 - 16:11

126

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Given $[0,1]\times [0,1]$ with $(s,0)\sim (s,1)$, prove that $f$ is well-defined and continuous

Published on 30 Dec 2016 - 22:38

1.9k

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Basis for the Quotient Topology

Published on 03 Jan 2017 - 20:41

453

Views

homeomorphic quotient spaces (with the complex projective plane)

Published on 08 Jan 2017 - 12:27

366

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Quotient Space, linear independent set of vectors

Published on 09 Jan 2017 - 18:50

40

Views

two layer separation is homeomorphic to inverse of second layer

Published on 10 Jan 2017 - 17:55

List Question

Why is $\mathbb{R}/(-1,1)$ not Hausdorff?

Injective implies surjective?

Prove a closed subspace has finite codimension

Is the limit $C_n[x]/I_n$ exsit when the dimension is infinite？

Figuring out what $\mathrm{O}(n)/\mathrm{SO}(n)$ is.

Quotient by squares of finite rank

Product of two quotient map need not be a quotient map

Showing that $\varphi: \overline{\mathbb{B}^2} \amalg \overline{\mathbb{B}^2} \to \mathbb{S}^2$ is a quotient map

Prove that $(X\times [0,1])/{\sim'}$ is homeomorphic to $(X/{\sim})\times[0,1].$

Indiscreet topology on quotient space

Given $[0,1]\times [0,1]$ with $(s,0)\sim (s,1)$, prove that $f$ is well-defined and continuous

Basis for the Quotient Topology

homeomorphic quotient spaces (with the complex projective plane)

Quotient Space, linear independent set of vectors

two layer separation is homeomorphic to inverse of second layer

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