List questions from quotient-spaces

Published on 30 Mar 2026 - 11:58

45

Views

proving a map to a product space is a quotient map

Published on 14 Jan 2022 - 15:43

314

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Quotient norm of a Banach space induces the quotient topology

Published on 16 Jan 2022 - 14:45

109

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The quotient space of a Banach space is a Banach space

Published on 18 Jan 2022 - 21:41

214

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Show that $\Bbb S^1 / {\sim}$ is homeomorphic to $I=[0,1]$.

Published on 18 Jan 2022 - 21:51

266

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Proving the isomorphism between subspaces of a vector space and subspaces of quotient spaces

Published on 19 Jan 2022 - 12:33

39

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Is restriction of a projection to a connected subset a quotient map?

Published on 28 Mar 2026 - 5:22

79

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Proving the existence of complement subspace using quotients

Published on 22 Jan 2022 - 9:13

85

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Can I see the category of objects over $X$ as a quotient?

Published on 24 Jan 2022 - 2:13

37

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Pullback of a line bundle on a stack amounts to a rational character

Published on 24 Feb 2026 - 7:36

159

Views

Normed Vector Space with Complete Subspace and Quotient Space

Published on 26 Jan 2022 - 6:02

69

Views

Let $\pi$ be the quotient map $S^n\to\mathbb R\mathrm{P}^n$. Is $\pi_{\star p}:T_pS^n\to T_{\pi(p)}\mathbb R\mathrm P^n$ an isomorphism?

Published on 28 Mar 2026 - 2:44

148

Views

Show that a Hausdorff space $X$ is regular if and only if $X/A$ is Hausdorff for all $A$ closed in $X$.

Published on 29 Mar 2026 - 12:11

25

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Compute the dimension of the quotient space $\mathfrak m_a/\mathfrak m_a^2$

Published on 25 Mar 2026 - 11:16

64

Views

When does a quotient of a subset coincide with a quotient of a set by the action of a group?

Published on 05 Apr 2026 - 5:10

List Question

Topological Dimension of Quotient Space

proving a map to a product space is a quotient map

Quotient norm of a Banach space induces the quotient topology

The quotient space of a Banach space is a Banach space

Show that $\Bbb S^1 / {\sim}$ is homeomorphic to $I=[0,1]$.

Proving the isomorphism between subspaces of a vector space and subspaces of quotient spaces

Is restriction of a projection to a connected subset a quotient map?

Proving the existence of complement subspace using quotients

Can I see the category of objects over $X$ as a quotient?

Pullback of a line bundle on a stack amounts to a rational character

Normed Vector Space with Complete Subspace and Quotient Space

Let $\pi$ be the quotient map $S^n\to\mathbb R\mathrm{P}^n$. Is $\pi_{\star p}:T_pS^n\to T_{\pi(p)}\mathbb R\mathrm P^n$ an isomorphism?

Show that a Hausdorff space $X$ is regular if and only if $X/A$ is Hausdorff for all $A$ closed in $X$.

Compute the dimension of the quotient space $\mathfrak m_a/\mathfrak m_a^2$

When does a quotient of a subset coincide with a quotient of a set by the action of a group?

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