Question

Convergence does not imply coordinate convergence

score 83 · Answer 1 · 2018-08-08 11:49:50

83

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Convergence does not imply coordinate convergence

Published on 08 Aug 2018 - 11:49

score 88 · Answer 2 · 2026-03-29 02:36:22

88

Views

Please, where can I find some good worked examples of compact spaces?

Published on 29 Mar 2026 - 2:36

score 172 · Answer 3 · 2026-03-26 01:00:37

172

Views

Are all Distance Metrics, Divergence Functions?

Published on 26 Mar 2026 - 1:00

score 356 · Answer 4 · 2026-03-21 23:59:08

356

Views

Compactness of sublevels

Published on 21 Mar 2026 - 23:59

score 59 · Answer 5 · 2018-08-08 18:23:52

59

Views

Closed subset of a metric space admits open subsets

Published on 08 Aug 2018 - 18:23

score 651 · Answer 6 · 2018-08-09 00:38:26

651

Views

Prove that if $A,B$ are closed then, $ \exists\;U,V$ open sets such that $U\cap V= \emptyset$

Published on 09 Aug 2018 - 0:38

score 664 · Answer 7 · 2026-03-25 16:45:25

664

Views

Help understanding the proof that $(C[0,1]), d_\infty$ is complete

Published on 25 Mar 2026 - 16:45

score 1.7k · Answer 8 · 2018-08-09 18:54:01

1.7k

Views

Prove that if $A,B$ are closed and disjoint in a metric space, then they are contained in disjoint neighborhoods

Published on 09 Aug 2018 - 18:54

score 142 · Answer 9 · 2018-08-09 21:47:59

142

Views

Distance between finite sets of points

Published on 09 Aug 2018 - 21:47

score 56 · Answer 10 · 2026-03-25 19:07:10

56

Views

Edit: Prove that $(U,\delta)$ is complete where $\delta(x,y)=d(x,y)+\Big|\frac{1}{d(x,F)}-\frac{1}{d(y,F)}\Big|,\;\;\forall\; x,y\in U$

Published on 25 Mar 2026 - 19:07

score 428 · Answer 11 · 2026-03-25 19:02:22

428

Views

$E$ be a normed vector space. Prove that $U+V$ is open in E

Published on 25 Mar 2026 - 19:02

score 75 · Answer 12 · 2026-03-25 19:02:57

75

Views

If $d_1\sim d_2$ and $I:(E,d_1)\to(E,d_2) $, prove that $I$ is continuous.

Published on 25 Mar 2026 - 19:02

score 61 · Answer 13 · 2026-03-25 04:40:29

61

Views

Permutation matrix preseves volume of a set in Euclidean space

Published on 25 Mar 2026 - 4:40

score 192 · Answer 14 · 2026-03-25 20:34:17

192

Views

Showing that a function is a contraction

Published on 25 Mar 2026 - 20:34

score 324 · Answer 15 · 2018-08-11 09:43:50

324

Views

Open ball in Discrete metric space

Published on 11 Aug 2018 - 9:43

List Question

Convergence does not imply coordinate convergence

Please, where can I find some good worked examples of compact spaces?

Are all Distance Metrics, Divergence Functions?

Compactness of sublevels

Closed subset of a metric space admits open subsets

Prove that if $A,B$ are closed then, $ \exists\;U,V$ open sets such that $U\cap V= \emptyset$

Help understanding the proof that $(C[0,1]), d_\infty$ is complete

Prove that if $A,B$ are closed and disjoint in a metric space, then they are contained in disjoint neighborhoods

Distance between finite sets of points

Edit: Prove that $(U,\delta)$ is complete where $\delta(x,y)=d(x,y)+\Big|\frac{1}{d(x,F)}-\frac{1}{d(y,F)}\Big|,\;\;\forall\; x,y\in U$

$E$ be a normed vector space. Prove that $U+V$ is open in E

If $d_1\sim d_2$ and $I:(E,d_1)\to(E,d_2) $, prove that $I$ is continuous.

Permutation matrix preseves volume of a set in Euclidean space

Showing that a function is a contraction

Open ball in Discrete metric space

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