List questions from metric-spaces

114

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Prove that the function $f:X\to I=[0,1]$ by $f(x)=\min\{\frac{d(x,C)}{d(p,C)},1\}$ is continuous on $X$.

Published on 25 Mar 2026 - 6:29

466

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Probability distribution to maximize the expected distance between two points

Published on 29 Mar 2026 - 3:02

313

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Does Cauchy Completeness imply the Heine-Borel theorem generally?

Published on 26 Mar 2026 - 6:25

32

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$V\colon \mathcal{B}(X, \mathbb{R}) \rightarrow \mathcal{B}(X, \mathbb{R})$, $V(f) = |f|$ is continuous

Published on 05 Feb 2019 - 10:37

63

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Metric space analog for manifold with boundary

Published on 25 Mar 2026 - 1:16

80

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Exchanging limits when functions may not converge uniformly

Published on 29 Mar 2026 - 4:09

401

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$\epsilon$ fattening of an open set needn't be open

Published on 31 Mar 2026 - 4:27

77

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Silly question on lower semi-continuity

Published on 23 Feb 2026 - 6:27

810

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Showing $\{(x, y) : x^{2} > y\}$ is an open set

Published on 06 Feb 2019 - 13:36

965

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Union of closed sets with empty interior

Published on 06 Feb 2019 - 16:58

121

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Discrete metric space and continuity.

Published on 06 Feb 2019 - 17:29

36

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What are convergent sequences in a given metric space?

Published on 06 Feb 2019 - 18:59

37

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Balls on boundary of a set

Published on 07 Feb 2019 - 1:37

187

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If $\text{Boundary}(A)\subseteq A.$, then $\overline A=A$?

Published on 07 Feb 2019 - 17:15

21

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How to define closeness measure between a matrix and its permuted smoothed version.

Published on 25 Mar 2026 - 19:04

List Question

Prove that the function $f:X\to I=[0,1]$ by $f(x)=\min\{\frac{d(x,C)}{d(p,C)},1\}$ is continuous on $X$.

Probability distribution to maximize the expected distance between two points

Does Cauchy Completeness imply the Heine-Borel theorem generally?

$V\colon \mathcal{B}(X, \mathbb{R}) \rightarrow \mathcal{B}(X, \mathbb{R})$, $V(f) = |f|$ is continuous

Metric space analog for manifold with boundary

Exchanging limits when functions may not converge uniformly

$\epsilon$ fattening of an open set needn't be open

Silly question on lower semi-continuity

Showing $\{(x, y) : x^{2} > y\}$ is an open set

Union of closed sets with empty interior

Discrete metric space and continuity.

What are convergent sequences in a given metric space?

Balls on boundary of a set

If $\text{Boundary}(A)\subseteq A.$, then $\overline A=A$?

How to define closeness measure between a matrix and its permuted smoothed version.

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