List questions from metric-spaces

Published on 14 Mar 2019 - 17:29

326

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Every isometry of a compact metric space into itself is onto

Published on 25 Mar 2026 - 12:52

223

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Hausdorff metric and connectedness

Published on 27 Mar 2026 - 11:58

582

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Why the length is lower semi-continuous?

Published on 23 Feb 2026 - 6:27

180

Views

Topology. In the $\ell^2$ space. Is the following set compact, bounded and/or closed?

Published on 02 Apr 2026 - 3:50

66

Views

Is the norm $||x||:= \sum\limits_{i=1}^{\infty} 2^{-i}|x_i|$ equivalent to usual norm in $l_2$?

Published on 02 Apr 2026 - 3:49

642

Views

Proof verification: Let $K$ be compact, then there exists disjoint open subsets $U,V \subset X$ so that $x \in U$ and $K \subset V$

Published on 31 Mar 2026 - 7:52

394

Views

Is the set of bounded functions connected?

Published on 29 Mar 2026 - 17:43

84

Views

Open ball in $M=\mathbb{R}\setminus\{-1,1\}$

Published on 15 Mar 2019 - 18:59

126

Views

To what extent are measure, topology, distances / norms related?

Published on 02 Apr 2026 - 3:49

252

Views

Not-too-non-compact metric spaces

Published on 16 Mar 2019 - 20:28

74

Views

Relationship between a metric and quantum mechanical matrices

Published on 27 Mar 2026 - 13:46

701

Views

How to prove the triangle inequality for this metric space

Published on 17 Mar 2019 - 2:53

123

Views

Difference between limit of function and continuous function in metric spaces

Published on 17 Mar 2019 - 21:33

1.2k

Views

How do we show that $||x||_{\infty}\leq||x||_1\leq n||x||_{\infty}$?

Published on 02 Apr 2026 - 5:25

List Question

Show that space is not metrizable

Every isometry of a compact metric space into itself is onto

Hausdorff metric and connectedness

Why the length is lower semi-continuous?

Topology. In the $\ell^2$ space. Is the following set compact, bounded and/or closed?

Is the norm $||x||:= \sum\limits_{i=1}^{\infty} 2^{-i}|x_i|$ equivalent to usual norm in $l_2$?

Proof verification: Let $K$ be compact, then there exists disjoint open subsets $U,V \subset X$ so that $x \in U$ and $K \subset V$

Is the set of bounded functions connected?

Open ball in $M=\mathbb{R}\setminus\{-1,1\}$

To what extent are measure, topology, distances / norms related?

Not-too-non-compact metric spaces

Relationship between a metric and quantum mechanical matrices

How to prove the triangle inequality for this metric space

Difference between limit of function and continuous function in metric spaces

How do we show that $||x||_{\infty}\leq||x||_1\leq n||x||_{\infty}$?

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