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What's the motivation behind metric spaces?

score 4.1k · Answer 1 · 2026-04-09 20:39:48

4.1k

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What's the motivation behind metric spaces?

Published on 09 Apr 2026 - 20:39

score 4.6k · Answer 2 · 2026-04-13 00:23:50

4.6k

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Product topology and standard euclidean topology over $\mathbb{R}^n$ are equivalent

Published on 13 Apr 2026 - 0:23

score 78 · Answer 3 · 2026-03-31 11:46:04

78

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What is the metric on ${(L^{p}(\Omega))}^N$? (prove that sobolev spaces uniformly convex)

Published on 31 Mar 2026 - 11:46

score 2.2k · Answer 4 · 2026-04-10 16:18:05

2.2k

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Is a closure a disjoint union of limit points and isolated points

Published on 10 Apr 2026 - 16:18

score 106 · Answer 5 · 2026-04-12 23:37:08

106

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basic question of topology involving compactness and convexity

Published on 12 Apr 2026 - 23:37

score 194 · Answer 6 · 2026-03-25 17:40:48

194

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Quasi-isometry of Schreier coset graphs

Published on 25 Mar 2026 - 17:40

score 56 · Answer 7 · 2026-04-01 14:07:09

56

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define distance in a manifold over the reals

Published on 01 Apr 2026 - 14:07

score 535 · Answer 8 · 2014-04-16 23:49:53

Let $M$ be a bounded subset of the space $C_{[a,b]}$. Prove that the set of all functions $F(x)=\int^{x}_{a}f(t)dt$ with $f\in{M}$ compact.

score 68 · Answer 9 · 2026-04-11 19:27:31

68

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Is there a name for this partial order between metrics?

Published on 11 Apr 2026 - 19:27

score 3.1k · Answer 10 · 2026-04-12 03:33:37

3.1k

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Show that $f(\bar A) \subset \overline{f(A)}$.

Published on 12 Apr 2026 - 3:33

score 1.7k · Answer 11 · 2026-03-27 01:46:42

1.7k

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Is the set of all integers with metric $d(m,n)=|m-n|$ a complete space?

Published on 27 Mar 2026 - 1:46

score 686 · Answer 12 · 2026-04-04 13:14:06

686

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Trouble finishing a (direct) proof that $\ell^2(A)$ is a complete metric space

Published on 04 Apr 2026 - 13:14

score 2.1k · Answer 13 · 2026-03-29 10:08:49

2.1k

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Is there a distance metric for dot product similarity that preserves the ordering of nearest neighbors?

Published on 29 Mar 2026 - 10:08

score 50 · Answer 14 · 2026-04-08 18:02:36

50

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A lemma on function spaces

Published on 08 Apr 2026 - 18:02

score 67 · Answer 15 · 2026-04-12 19:16:32

67

Views

To show closedness of a subset in a metric spaces

Published on 12 Apr 2026 - 19:16

List Question

What's the motivation behind metric spaces?

Product topology and standard euclidean topology over $\mathbb{R}^n$ are equivalent

What is the metric on ${(L^{p}(\Omega))}^N$? (prove that sobolev spaces uniformly convex)

Is a closure a disjoint union of limit points and isolated points

basic question of topology involving compactness and convexity

Quasi-isometry of Schreier coset graphs

define distance in a manifold over the reals

Let $M$ be a bounded subset of the space $C_{[a,b]}$. Prove that the set of all functions $F(x)=\int^{x}_{a}f(t)dt$ with $f\in{M}$ compact.

Is there a name for this partial order between metrics?

Show that $f(\bar A) \subset \overline{f(A)}$.

Is the set of all integers with metric $d(m,n)=|m-n|$ a complete space?

Trouble finishing a (direct) proof that $\ell^2(A)$ is a complete metric space

Is there a distance metric for dot product similarity that preserves the ordering of nearest neighbors?

A lemma on function spaces

To show closedness of a subset in a metric spaces

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