List questions from metric-spaces

Published on 01 Apr 2026 - 5:02

176

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Pointlike function without minimum.

Published on 16 Oct 2018 - 16:12

1.1k

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How to show that $A \subset X$ is totally bounded $\iff$ $\bar{A}$ is totally bounded.

Published on 16 Oct 2018 - 19:00

107

Views

Another way to prove $d(x,y)$ is a metric

Published on 16 Oct 2018 - 20:59

177

Views

Intersection of any number of compact sets is compact.

Published on 29 Mar 2026 - 15:59

27

Views

Problem with inequality proof with metrics.

Published on 17 Oct 2018 - 12:12

61

Views

Is sets being zero distance apart a topological property?

Published on 18 Oct 2018 - 6:36

190

Views

Show $A$ is compact subset of a metric space $(X,\mathscr T, d)$ only if for all $x \in X$, $d(x,A)=d(x,a)$ for some $a \in A$.

Published on 29 Mar 2026 - 16:00

944

Views

Properties of sum of two metrics

Published on 18 Oct 2018 - 12:11

78

Views

Metric with stronger constraint on the triangle inequality

Published on 18 Oct 2018 - 19:22

832

Views

Distance between boundary and interior of a set is zero

Published on 19 Oct 2018 - 1:41

37

Views

Limit of Convergent Sequences in a Compact Graph when the Domain is Compact

Published on 19 Oct 2018 - 3:12

366

Views

Detail in Perelman's proof of the Soul Conjecture: why $O(\delta^2)$ and not $O(\delta)$?

Published on 25 Mar 2026 - 14:25

307

Views

Inseparable complete metric space with full Radon probability measure

Published on 25 Mar 2026 - 9:48

43

Views

Mapping the cycle graph into the real line

Published on 02 Apr 2026 - 22:07

List Question

Metrics on families of functions

Pointlike function without minimum.

How to show that $A \subset X$ is totally bounded $\iff$ $\bar{A}$ is totally bounded.

Another way to prove $d(x,y)$ is a metric

Intersection of any number of compact sets is compact.

Problem with inequality proof with metrics.

Is sets being zero distance apart a topological property?

Show $A$ is compact subset of a metric space $(X,\mathscr T, d)$ only if for all $x \in X$, $d(x,A)=d(x,a)$ for some $a \in A$.

Properties of sum of two metrics

Metric with stronger constraint on the triangle inequality

Distance between boundary and interior of a set is zero

Limit of Convergent Sequences in a Compact Graph when the Domain is Compact

Detail in Perelman's proof of the Soul Conjecture: why $O(\delta^2)$ and not $O(\delta)$?

Inseparable complete metric space with full Radon probability measure

Mapping the cycle graph into the real line

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