Question

Every sequentially compact space is countably compact

score 2.5k · Answer 1 · 2026-04-09 08:58:36

2.5k

Views

Every sequentially compact space is countably compact

Published on 09 Apr 2026 - 8:58

score 87 · Answer 2 · 2026-04-14 10:18:13

87

Views

Shift of first category set in a compact metric space.

Published on 14 Apr 2026 - 10:18

score 374 · Answer 3 · 2026-04-13 11:10:33

374

Views

Locally compact Hausdorff and Second countable space and nested compact sequences

Published on 13 Apr 2026 - 11:10

score 744 · Answer 4 · 2026-04-21 05:05:01

744

Views

When is $C(X)$ reflexive?

Published on 21 Apr 2026 - 5:05

score 285 · Answer 5 · 2026-04-13 14:01:03

285

Views

One point compactification of uncountable set with discrete topology cannot be imbedded into $\mathbb{R}^{2}$?

Published on 13 Apr 2026 - 14:01

score 345 · Answer 6 · 2026-04-12 16:47:16

345

Views

To prove that if a function $f : \mathbb R \to \mathbb R$ is locally increasing at every point then the function is increasing

Published on 12 Apr 2026 - 16:47

score 79 · Answer 7 · 2026-04-12 02:35:33

79

Views

Difficulty in choosing correct answer among the options.

Published on 12 Apr 2026 - 2:35

score 313 · Answer 8 · 2026-04-11 19:02:40

313

Views

Is it true that the closed convex hull of a compact subset of the dual equipped with the w*-topology is compact?

Published on 11 Apr 2026 - 19:02

score 89 · Answer 9 · 2026-04-14 16:48:19

89

Views

Motivation and intuition behind concept of totally bounded-ness in metric spaces

Published on 14 Apr 2026 - 16:48

score 1.1k · Answer 10 · 2026-04-15 22:24:13

1.1k

Views

A set is compact iff all closed collections of subsets with the f.i.p. have nonempty intersection

Published on 15 Apr 2026 - 22:24

score 329 · Answer 11 · 2026-04-15 09:13:19

329

Views

Showing the continuity of $d(x,f(x))$

Published on 15 Apr 2026 - 9:13

score 369 · Answer 12 · 2026-04-12 22:41:14

369

Views

Compactness and sequential compactness are equivalent in metric space but not always in others

Published on 12 Apr 2026 - 22:41

score 828 · Answer 13 · 2026-04-13 11:49:51

828

Views

Is any closed ball compact in the Weak$^$ topology $\sigma(E^,E)$ for a Banach Space $E$?

Published on 13 Apr 2026 - 11:49

score 86 · Answer 14 · 2026-04-10 22:59:25

86

Views

Is there a name for a topological space $X$ in which every proper closed subset is compact?

Published on 10 Apr 2026 - 22:59

score 251 · Answer 15 · 2026-04-15 22:59:22

251

Views

Sequences of 0s and 1s are compact

Published on 15 Apr 2026 - 22:59

List Question

Every sequentially compact space is countably compact

Shift of first category set in a compact metric space.

Locally compact Hausdorff and Second countable space and nested compact sequences

When is $C(X)$ reflexive?

One point compactification of uncountable set with discrete topology cannot be imbedded into $\mathbb{R}^{2}$?

To prove that if a function $f : \mathbb R \to \mathbb R$ is locally increasing at every point then the function is increasing

Difficulty in choosing correct answer among the options.

Is it true that the closed convex hull of a compact subset of the dual equipped with the w*-topology is compact?

Motivation and intuition behind concept of totally bounded-ness in metric spaces

A set is compact iff all closed collections of subsets with the f.i.p. have nonempty intersection

Showing the continuity of $d(x,f(x))$

Compactness and sequential compactness are equivalent in metric space but not always in others

Is any closed ball compact in the Weak$^$ topology $\sigma(E^,E)$ for a Banach Space $E$?

Is there a name for a topological space $X$ in which every proper closed subset is compact?

Sequences of 0s and 1s are compact

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