Question

If $K$ compact then $K$ is closed (a proof by sequences)

score 1k · Answer 1 · 2026-03-28 06:48:24

1k

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If $K$ compact then $K$ is closed (a proof by sequences)

Published on 28 Mar 2026 - 6:48

score 52 · Answer 2 · 2018-05-16 07:20:50

52

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Compactness of a set of distances

Published on 16 May 2018 - 7:20

score 106 · Answer 3 · 2018-05-16 14:56:00

106

Views

What's the usual sigma-algebra on $\mathbb R^\infty$?

Published on 16 May 2018 - 14:56

score 42 · Answer 4 · 2018-05-16 23:42:52

For closed $(S_n)_{n\in\mathbb{N}}$ in $\mathbb{R}^n$ and $S:=\bigcup_{n\in\mathbb{N}}S_n$, if $S°\neq0 $ then $S_n°\neq0$ for some $n \in \mathbb{N}$

score 48 · Answer 5 · 2018-05-18 11:00:34

48

Views

Given a metric space, $U$ an open cover, is $r(x)$ necessarily continuous?

Published on 18 May 2018 - 11:00

score 107 · Answer 6 · 2018-05-18 14:13:24

107

Views

Distance function for closeness among rectangles.

Published on 18 May 2018 - 14:13

score 229 · Answer 7 · 2018-05-19 08:52:58

229

Views

Soft question: what is the intuition behind labeling of metrics?

Published on 19 May 2018 - 8:52

score 73 · Answer 8 · 2026-03-25 10:55:34

73

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Sequence of points in metric space

Published on 25 Mar 2026 - 10:55

score 58 · Answer 9 · 2018-05-19 16:20:33

If $G_1, G_2$ be two open sets in the usual metric space $(\mathbb{R}, d_1)$ can $G_1\times G_2$ be open in $\mathbb{R}^2$?

score 43 · Answer 10 · 2018-05-19 16:40:19

43

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Proof Verification: Suppose $X$ is a metric space and $S\subseteq X$. Then $\partial (\partial S)\subseteq \partial S$

Published on 19 May 2018 - 16:40

score 26 · Answer 11 · 2018-05-20 09:14:14

26

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Limit of the pair of the sequences is the pair of the limits of the sequences

Published on 20 May 2018 - 9:14

score 39 · Answer 12 · 2026-03-25 10:55:25

39

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Proving sequence of half isometries on a compact has converging subsequence to fixed point

Published on 25 Mar 2026 - 10:55

score 314 · Answer 13 · 2018-05-20 18:03:17

314

Views

Completeness preserved under homeomorphism.

Published on 20 May 2018 - 18:03

score 221 · Answer 14 · 2018-05-20 22:50:42

221

Views

Space of Bounded Functions - Distance Function

Published on 20 May 2018 - 22:50

score 360 · Answer 15 · 2018-05-21 11:02:16

360

Views

Prove unit ball is closed and bounded

Published on 21 May 2018 - 11:02

List Question

If $K$ compact then $K$ is closed (a proof by sequences)

Compactness of a set of distances

What's the usual sigma-algebra on $\mathbb R^\infty$?

For closed $(S_n)_{n\in\mathbb{N}}$ in $\mathbb{R}^n$ and $S:=\bigcup_{n\in\mathbb{N}}S_n$, if $S°\neq0 $ then $S_n°\neq0$ for some $n \in \mathbb{N}$

Given a metric space, $U$ an open cover, is $r(x)$ necessarily continuous?

Distance function for closeness among rectangles.

Soft question: what is the intuition behind labeling of metrics?

Sequence of points in metric space

If $G_1, G_2$ be two open sets in the usual metric space $(\mathbb{R}, d_1)$ can $G_1\times G_2$ be open in $\mathbb{R}^2$?

Proof Verification: Suppose $X$ is a metric space and $S\subseteq X$. Then $\partial (\partial S)\subseteq \partial S$

Limit of the pair of the sequences is the pair of the limits of the sequences

Proving sequence of half isometries on a compact has converging subsequence to fixed point

Completeness preserved under homeomorphism.

Space of Bounded Functions - Distance Function

Prove unit ball is closed and bounded

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