Question

Prove that this space is compact/not compact by using Arzelà–Ascoli theorem

score 74 · Answer 1 · 2019-05-10 19:57:53

74

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Prove that this space is compact/not compact by using Arzelà–Ascoli theorem

Published on 10 May 2019 - 19:57

score 528 · Answer 2 · 2019-05-11 23:17:51

528

Views

Two disjoint closed sets $A,B$ with $B$ compact, show $d(A,B) > 0$ Verify my proof

Published on 11 May 2019 - 23:17

score 47 · Answer 3 · 2019-05-12 09:02:07

47

Views

Does the given set is compact in $\mathbb{R^{2}}$?

Published on 12 May 2019 - 9:02

score 572 · Answer 4 · 2026-03-29 07:30:32

572

Views

Counterexample for "continuous image of closed and bounded is closed and bounded" (in normed spaces).

Published on 29 Mar 2026 - 7:30

score 2.1k · Answer 5 · 2019-05-12 16:06:33

2.1k

Views

Visual representation of difference between closed, bounded and compact sets

Published on 12 May 2019 - 16:06

score 100 · Answer 6 · 2026-03-25 06:22:10

100

Views

In a locally compact 2nd-countable Hausdorff space $E$ there is a sequence of compact subsets $K_n$ with $K_{n-1}⊆\overset∘{K_n}$ and $\bigcup_nK_n=E$

Published on 25 Mar 2026 - 6:22

score 393 · Answer 7 · 2026-03-29 07:33:47

393

Views

Compactness in the space of all real null sequences

Published on 29 Mar 2026 - 7:33

score 60 · Answer 8 · 2019-05-15 02:50:46

60

Views

Is every metric space compact?

Published on 15 May 2019 - 2:50

score 718 · Answer 9 · 2019-05-16 23:28:24

718

Views

Covering a compact set with balls whose centers do not belong to other balls.

Published on 16 May 2019 - 23:28

score 52 · Answer 10 · 2019-05-18 08:03:22

52

Views

On the dimension of rationals over real numbers

Published on 18 May 2019 - 8:03

score 129 · Answer 11 · 2026-03-29 08:13:44

129

Views

Example of noncompact space in which every real valued continuous function on it is uniformly continuous

Published on 29 Mar 2026 - 8:13

score 47 · Answer 12 · 2019-05-18 13:40:04

47

Views

Is there a name for this notion of "radius of compactness" in a metric space?

Published on 18 May 2019 - 13:40

score 127 · Answer 13 · 2026-03-26 03:10:36

127

Views

Prove that this operator is compact

Published on 26 Mar 2026 - 3:10

score 382 · Answer 14 · 2026-03-27 22:01:36

382

Views

Let $f:K \rightarrow N$ be a continuous function from a compact $K$. Show that $f$ is uniformly continuous

Published on 27 Mar 2026 - 22:01

score 202 · Answer 15 · 2026-03-25 15:09:48

202

Views

Using Alexander lemma to prove that if $X$ is continuum then the hyperspace $2^X$ is compact

Published on 25 Mar 2026 - 15:09

List Question

Prove that this space is compact/not compact by using Arzelà–Ascoli theorem

Two disjoint closed sets $A,B$ with $B$ compact, show $d(A,B) > 0$ Verify my proof

Does the given set is compact in $\mathbb{R^{2}}$?

Counterexample for "continuous image of closed and bounded is closed and bounded" (in normed spaces).

Visual representation of difference between closed, bounded and compact sets

In a locally compact 2nd-countable Hausdorff space $E$ there is a sequence of compact subsets $K_n$ with $K_{n-1}⊆\overset∘{K_n}$ and $\bigcup_nK_n=E$

Compactness in the space of all real null sequences

Is every metric space compact?

Covering a compact set with balls whose centers do not belong to other balls.

On the dimension of rationals over real numbers

Example of noncompact space in which every real valued continuous function on it is uniformly continuous

Is there a name for this notion of "radius of compactness" in a metric space?

Prove that this operator is compact

Let $f:K \rightarrow N$ be a continuous function from a compact $K$. Show that $f$ is uniformly continuous

Using Alexander lemma to prove that if $X$ is continuum then the hyperspace $2^X$ is compact

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