List questions from quotient-spaces

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Zero vector in quotient space

Published on 16 Oct 2020 - 0:56

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A invertible iff both restrictions are invertible

Published on 26 Mar 2026 - 19:18

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Show that the quotient space is not Hausdorff.

Published on 28 Mar 2026 - 15:26

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How to describe the embedding?

Published on 22 Oct 2020 - 14:00

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Quotient space of $\mathcal{l}^{\infty}$

Published on 22 Oct 2020 - 20:09

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Let $D^2 =\{\sqrt{x^2+y^2} \leq 1\} \subseteq \mathbb{R}^2$. Prove that $\mathbb{R}^2/D^2$ is homeomorphic to $\mathbb{R}^2$.

Published on 22 Oct 2020 - 20:26

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Doubt - Quotient map

Published on 23 Oct 2020 - 3:04

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Proof - $\mathbb S^1 \cong \mathbb S^1/ \mathbb Z_n$.

Published on 24 Oct 2020 - 20:41

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Let $ (X, \tau) $ be a paracompact space $ T_2 $ and $ A \subset X $. If $A$ is closed, then the quotient space $X / A$ is paracompact and $T_2$.

Published on 23 Feb 2026 - 6:25

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Question about the map $S^1\to S^1$ in the context of the real projective plane $\mathbb{R}P^2$

Published on 02 Apr 2026 - 5:06

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Prove fundamental group of R/~ is isomorphic to Z

Published on 28 Mar 2026 - 18:55

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Is the $S^1$ cone $D^2$?

Published on 29 Oct 2020 - 15:15

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Describe the quotient space that results from the partition of $\mathbb{R}$ into the equivalence classes on $\mathbb{R}$ given by $x-y\in \mathbb{Z}$

Published on 29 Oct 2020 - 20:50

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Some topological properties of "countable lines with one origin"

Published on 26 Mar 2026 - 1:28

List Question

$H$ closed implies $G / H$ Hausdorff

Zero vector in quotient space

A invertible iff both restrictions are invertible

Show that the quotient space is not Hausdorff.

How to describe the embedding?

Quotient space of $\mathcal{l}^{\infty}$

Let $D^2 =\{\sqrt{x^2+y^2} \leq 1\} \subseteq \mathbb{R}^2$. Prove that $\mathbb{R}^2/D^2$ is homeomorphic to $\mathbb{R}^2$.

Doubt - Quotient map

Proof - $\mathbb S^1 \cong \mathbb S^1/ \mathbb Z_n$.

Let $ (X, \tau) $ be a paracompact space $ T_2 $ and $ A \subset X $. If $A$ is closed, then the quotient space $X / A$ is paracompact and $T_2$.

Question about the map $S^1\to S^1$ in the context of the real projective plane $\mathbb{R}P^2$

Prove fundamental group of R/~ is isomorphic to Z

Is the $S^1$ cone $D^2$?

Describe the quotient space that results from the partition of $\mathbb{R}$ into the equivalence classes on $\mathbb{R}$ given by $x-y\in \mathbb{Z}$

Some topological properties of "countable lines with one origin"

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