Question

Prove that a subset in Hilbert space is open

score 232 · Answer 1 · 2026-03-27 13:47:15

232

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Prove that a subset in Hilbert space is open

Published on 27 Mar 2026 - 13:47

score 1.5k · Answer 2 · 2018-09-14 16:05:17

1.5k

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How to tell if a set is bounded? And the difference between a ball and sphere?

Published on 14 Sep 2018 - 16:05

score 1k · Answer 3 · 2018-09-14 17:12:04

1k

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Prove that every subset of a metric space $M$ can be written as the intersection of open sets.

Published on 14 Sep 2018 - 17:12

score 266 · Answer 4 · 2026-02-23 06:38:09

266

Views

prove the following lemma about a compact space and a ultrametric.

Published on 23 Feb 2026 - 6:38

score 143 · Answer 5 · 2026-03-23 11:12:04

143

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To check whether given space is metrizable

Published on 23 Mar 2026 - 11:12

score 52 · Answer 6 · 2018-09-15 01:35:57

52

Views

Open sets and open balls in a metric space

Published on 15 Sep 2018 - 1:35

score 443 · Answer 7 · 2018-09-15 08:04:49

443

Views

Changing the distance considered on a metric space changes open sets inside?

Published on 15 Sep 2018 - 8:04

score 100 · Answer 8 · 2018-09-15 12:06:17

100

Views

Show that $\{ x = (x_n) \in H^\infty: |x_k| < 1, k = 1, …, N\}$ is open in $H^\infty$

Published on 15 Sep 2018 - 12:06

score 77 · Answer 9 · 2018-09-15 16:19:38

77

Views

$(\mathbb{Q},|\cdot|_{\mathbb{Q}})$ is not connected

Published on 15 Sep 2018 - 16:19

score 984 · Answer 10 · 2018-09-15 18:12:12

984

Views

Is empty set with usual metric space $(X=\mathbb{R},d)$ bounded?

Published on 15 Sep 2018 - 18:12

score 390 · Answer 11 · 2026-03-25 17:36:13

390

Views

Homework question on convergence using the p-adic metric

Published on 25 Mar 2026 - 17:36

score 4.9k · Answer 12 · 2018-09-16 14:34:04

4.9k

Views

How is 0 a limit point of $\{1/n\}_{n=1}^{\infty}$?

Published on 16 Sep 2018 - 14:34

score 866 · Answer 13 · 2026-03-25 01:25:58

866

Views

How could one geometrically visualize any given metric space $(X,d)$?

Published on 25 Mar 2026 - 1:25

score 112 · Answer 14 · 2018-09-17 12:46:01

112

Views

Checking whether $X=\mathbb R$ with $d(x,y)=\min\{ \sqrt{|x-y|},|x-y|^2\}$ is a metric space

Published on 17 Sep 2018 - 12:46

score 439 · Answer 15 · 2026-03-26 03:01:32

439

Views

To show the two metrics induce the same topology but only one of them is complete

Published on 26 Mar 2026 - 3:01

List Question

Prove that a subset in Hilbert space is open

How to tell if a set is bounded? And the difference between a ball and sphere?

Prove that every subset of a metric space $M$ can be written as the intersection of open sets.

prove the following lemma about a compact space and a ultrametric.

To check whether given space is metrizable

Open sets and open balls in a metric space

Changing the distance considered on a metric space changes open sets inside?

Show that $\{ x = (x_n) \in H^\infty: |x_k| < 1, k = 1, …, N\}$ is open in $H^\infty$

$(\mathbb{Q},|\cdot|_{\mathbb{Q}})$ is not connected

Is empty set with usual metric space $(X=\mathbb{R},d)$ bounded?

Homework question on convergence using the p-adic metric

How is 0 a limit point of $\{1/n\}_{n=1}^{\infty}$?

How could one geometrically visualize any given metric space $(X,d)$?

Checking whether $X=\mathbb R$ with $d(x,y)=\min\{ \sqrt{|x-y|},|x-y|^2\}$ is a metric space

To show the two metrics induce the same topology but only one of them is complete

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