Question

Uniformly continuous imply bounded

score 270 · Answer 1 · 2026-03-25 15:38:23

270

Views

Uniformly continuous imply bounded

Published on 25 Mar 2026 - 15:38

score 303 · Answer 2 · 2026-03-30 01:15:17

303

Views

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

Published on 30 Mar 2026 - 1:15

score 52 · Answer 3 · 2019-03-28 20:17:43

52

Views

Compactness implies countably compactness

Published on 28 Mar 2019 - 20:17

score 245 · Answer 4 · 2019-03-29 06:32:49

245

Views

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

Published on 29 Mar 2019 - 6:32

score 350 · Answer 5 · 2026-03-26 19:17:11

350

Views

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

Published on 26 Mar 2026 - 19:17

score 392 · Answer 6 · 2019-03-30 08:41:43

392

Views

Regularity of measure on locally compact separable metric space

Published on 30 Mar 2019 - 8:41

score 118 · Answer 7 · 2019-03-30 15:00:42

118

Views

Is a compact union of compact spaces still compact?

Published on 30 Mar 2019 - 15:00

score 43 · Answer 8 · 2019-03-30 19:28:07

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 42 · Answer 9 · 2019-03-30 20:59:19

42

Views

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

Published on 30 Mar 2019 - 20:59

score 897 · Answer 10 · 2026-03-25 08:07:50

897

Views

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

Published on 25 Mar 2026 - 8:07

score 616 · Answer 11 · 2019-03-31 03:52:36

616

Views

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

Published on 31 Mar 2019 - 3:52

score 68 · Answer 12 · 2026-03-25 04:55:34

68

Views

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

Published on 25 Mar 2026 - 4:55

score 451 · Answer 13 · 2019-03-31 14:41:04

451

Views

Relatively compact and compact set exercise

Published on 31 Mar 2019 - 14:41

score 101 · Answer 14 · 2026-03-30 09:49:41

101

Views

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

Published on 30 Mar 2026 - 9:49

score 1.9k · Answer 15 · 2019-04-02 18:25:53

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 02 Apr 2019 - 18:25

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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