List questions from metric-spaces

Published on 25 Mar 2026 - 6:29

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Embedding a torus

Published on 24 Sep 2018 - 23:16

72

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Compact set in metric space

Published on 26 Mar 2026 - 4:29

198

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Are $L^p$ spaces connected?

Published on 29 Mar 2026 - 1:33

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Set of bounded functions closed in B(X,R)

Published on 25 Sep 2018 - 4:37

89

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Open Sets in Metric Topology

Published on 25 Sep 2018 - 11:23

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there is an $R >0$ such that $d(x , C) < R$ implies $x \in O$. Hint: use the Heine-Borel theorem.

Published on 25 Sep 2018 - 12:52

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Diameter hypothesis of Cantor's Intersection Theorem on a complete metric space.

Published on 25 Mar 2026 - 18:51

264

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In a metric space $(M,d)$, any Cauchy sequence $\{a_n\}_{n \in \mathbb{N}}$ in $M$ is convergent?

Published on 26 Sep 2018 - 2:07

310

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Does the sequence lemma hold for Hausdorff?

Published on 26 Sep 2018 - 11:18

117

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Completeness in metric spaces.

Published on 26 Sep 2018 - 11:37

295

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How to find disjoint neighborhoods of distinct points in a metric space?

Published on 26 Sep 2018 - 16:37

581

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How to prove the set of bounded sequences is clopen in the uniform metric?

Published on 26 Mar 2026 - 17:46

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Prove that $[0,\pi/2]$ is $d$-complete, where $d(x,y)=\left|\sin(x-y)\right|$.

Published on 25 Mar 2026 - 18:47

793

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Prove that $\mathbb{R}$ is homeomorphic to $(0,1)$

Published on 27 Sep 2018 - 5:34

List Question

Is the Schwarzschild singularity stretched in space as a straight line?

Embedding a torus

Compact set in metric space

Are $L^p$ spaces connected?

Set of bounded functions closed in B(X,R)

Open Sets in Metric Topology

there is an $R >0$ such that $d(x , C) < R$ implies $x \in O$. Hint: use the Heine-Borel theorem.

Diameter hypothesis of Cantor's Intersection Theorem on a complete metric space.

In a metric space $(M,d)$, any Cauchy sequence $\{a_n\}_{n \in \mathbb{N}}$ in $M$ is convergent?

Does the sequence lemma hold for Hausdorff?

Completeness in metric spaces.

How to find disjoint neighborhoods of distinct points in a metric space?

How to prove the set of bounded sequences is clopen in the uniform metric?

Prove that $[0,\pi/2]$ is $d$-complete, where $d(x,y)=\left|\sin(x-y)\right|$.

Prove that $\mathbb{R}$ is homeomorphic to $(0,1)$

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