Question

Uniformly continuous imply bounded

score 272 · Answer 1 · 2026-05-10 23:32:04

272

Views

Uniformly continuous imply bounded

Published on 10 May 2026 - 23:32

score 306 · Answer 2 · 2026-05-14 17:45:24

306

Views

Prove that Sequentially Compact Metric Spaces are Lindelöf without the Axiom of Choice.

Published on 14 May 2026 - 17:45

score 54 · Answer 3 · 2026-04-13 15:12:24

54

Views

Compactness implies countably compactness

Published on 13 Apr 2026 - 15:12

score 248 · Answer 4 · 2026-04-15 21:27:56

248

Views

Let X be sequentially compact. Then X is also countably compact.

Published on 15 Apr 2026 - 21:27

score 352 · Answer 5 · 2026-04-14 06:20:38

352

Views

A quotient space by group action is manifold $???$

Published on 14 Apr 2026 - 6:20

score 397 · Answer 6 · 2026-04-17 07:50:25

397

Views

Regularity of measure on locally compact separable metric space

Published on 17 Apr 2026 - 7:50

score 121 · Answer 7 · 2026-04-08 19:05:32

121

Views

Is a compact union of compact spaces still compact?

Published on 08 Apr 2026 - 19:05

score 46 · Answer 8 · 2026-04-16 16:05:42

Compactness of a set : $A=\left\lbrace 2019,1010,\ldots,(n+2018)/n,\ldots \right\rbrace$ and $B=A \cup \left\lbrace 1 \right\rbrace$

score 45 · Answer 9 · 2026-04-15 13:21:28

45

Views

Show that $S_R := \{x \in \mathbb{R}^n : \|DL_x\| = R\}$ is compact

Published on 15 Apr 2026 - 13:21

score 899 · Answer 10 · 2026-05-11 02:47:12

899

Views

Inverse image of singleton sets under continuous map between compact Hausdorff topological spaces

Published on 11 May 2026 - 2:47

score 619 · Answer 11 · 2026-04-16 11:26:42

619

Views

X is sequentially compact $\implies $ then Lebesgue lemma hold for X where X is metric space

Published on 16 Apr 2026 - 11:26

score 72 · Answer 12 · 2026-05-10 17:36:04

72

Views

Is the set $\overline{\text{conv}}^{w^} C$ weakly compact?

Published on 10 May 2026 - 17:36

score 454 · Answer 13 · 2026-04-08 22:56:26

454

Views

Relatively compact and compact set exercise

Published on 08 Apr 2026 - 22:56

score 103 · Answer 14 · 2026-04-14 01:57:28

103

Views

Noncompactness of $L^{p}$ space in $[-1,1]$ interval

Published on 14 Apr 2026 - 1:57

score 1.9k · Answer 15 · 2026-04-15 12:31:02

1.9k

Views

Prove that for each $\epsilon>0$, there exist a compact $K\subset E$ such that $m(E\cap K^c)<\epsilon$

Published on 15 Apr 2026 - 12:31

List Question

Uniformly continuous imply bounded

Prove that Sequentially Compact Metric Spaces are Lindelöf without the Axiom of Choice.

Compactness implies countably compactness

Let X be sequentially compact. Then X is also countably compact.

A quotient space by group action is manifold $???$

Regularity of measure on locally compact separable metric space

Is a compact union of compact spaces still compact?

Compactness of a set : $A=\left\lbrace 2019,1010,\ldots,(n+2018)/n,\ldots \right\rbrace$ and $B=A \cup \left\lbrace 1 \right\rbrace$

Show that $S_R := \{x \in \mathbb{R}^n : \|DL_x\| = R\}$ is compact

Inverse image of singleton sets under continuous map between compact Hausdorff topological spaces

X is sequentially compact $\implies $ then Lebesgue lemma hold for X where X is metric space

Is the set $\overline{\text{conv}}^{w^} C$ weakly compact?

Relatively compact and compact set exercise

Noncompactness of $L^{p}$ space in $[-1,1]$ interval

Prove that for each $\epsilon>0$, there exist a compact $K\subset E$ such that $m(E\cap K^c)<\epsilon$

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