Question

Example of a first-countable non-$T_1$ compact topological space which is not sequentially compact?

score 189 · Answer 1 · 2026-04-04 04:37:48

189

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Example of a first-countable non-$T_1$ compact topological space which is not sequentially compact?

Published on 04 Apr 2026 - 4:37

score 329 · Answer 2 · 2026-03-25 06:01:44

329

Views

Surjective nonexpanding map between metric spaces with the same diameter is an isometry?

Published on 25 Mar 2026 - 6:01

score 1.3k · Answer 3 · 2016-09-04 16:32:20

1.3k

Views

Open sets with compact closure containing a given compact set

Published on 04 Sep 2016 - 16:32

score 192 · Answer 4 · 2026-03-25 11:16:30

192

Views

If every point of a compact Hausdorff space is the intersection of a nested sequence of open sets then is the space first-countable?

Published on 25 Mar 2026 - 11:16

score 66 · Answer 5 · 2026-03-26 07:46:30

66

Views

$X,Y$ be locally compact spaces , then is $X \times Y$ also locally compact?

Published on 26 Mar 2026 - 7:46

score 72 · Answer 6 · 2016-09-06 12:27:34

72

Views

Convergence of probability and compactness

Published on 06 Sep 2016 - 12:27

score 2.1k · Answer 7 · 2026-02-23 04:56:24

2.1k

Views

Interval $[0,1]$ is neither compact nor connected in the Sorgenfrey line.

Published on 23 Feb 2026 - 4:56

score 188 · Answer 8 · 2026-03-28 03:25:36

188

Views

Question about compactness in quotient space.

Published on 28 Mar 2026 - 3:25

score 1.4k · Answer 9 · 2016-09-12 20:36:06

1.4k

Views

Proving that compactness implies the Finite Intersection Property

Published on 12 Sep 2016 - 20:36

score 410 · Answer 10 · 2016-09-13 17:10:58

410

Views

Non-empty compact subset of an open set?

Published on 13 Sep 2016 - 17:10

score 3.3k · Answer 11 · 2016-09-15 00:04:02

3.3k

Views

Understanding relative compactness of a sequence of functions

Published on 15 Sep 2016 - 0:04

score 79 · Answer 12 · 2016-09-17 01:26:01

79

Views

Question of proof about a compact space if and only if every infinite subset have an acumulation point

Published on 17 Sep 2016 - 1:26

score 132 · Answer 13 · 2026-03-28 02:09:36

132

Views

Compact modulo subgroup definition

Published on 28 Mar 2026 - 2:09

score 3.2k · Answer 14 · 2026-02-23 12:06:18

3.2k

Views

Why is an equicontinuous and pointwise bounded sequence of real-valued functions on a compact metric space uniformly bounded?

Published on 23 Feb 2026 - 12:06

score 317 · Answer 15 · 2026-04-04 17:55:44

317

Views

Characterisation of Compact Subsets in Banach Spaces

Published on 04 Apr 2026 - 17:55

List Question

Example of a first-countable non-$T_1$ compact topological space which is not sequentially compact?

Surjective nonexpanding map between metric spaces with the same diameter is an isometry?

Open sets with compact closure containing a given compact set

If every point of a compact Hausdorff space is the intersection of a nested sequence of open sets then is the space first-countable?

$X,Y$ be locally compact spaces , then is $X \times Y$ also locally compact?

Convergence of probability and compactness

Interval $[0,1]$ is neither compact nor connected in the Sorgenfrey line.

Question about compactness in quotient space.

Proving that compactness implies the Finite Intersection Property

Non-empty compact subset of an open set?

Understanding relative compactness of a sequence of functions

Question of proof about a compact space if and only if every infinite subset have an acumulation point

Compact modulo subgroup definition

Why is an equicontinuous and pointwise bounded sequence of real-valued functions on a compact metric space uniformly bounded?

Characterisation of Compact Subsets in Banach Spaces

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