Question

Properties of Infinite set on co-finite topology and Countable set on co-countable topology

score 1k · Answer 1 · 2016-06-15 05:03:48

1k

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Properties of Infinite set on co-finite topology and Countable set on co-countable topology

Published on 15 Jun 2016 - 5:03

score 843 · Answer 2 · 2013-04-27 17:13:26

843

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$X$ second countable locally compact Hausdorff implies $C(X)$ separable?

Published on 27 Apr 2013 - 17:13

score 17.8k · Answer 3 · 2013-07-01 06:53:29

17.8k

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A metric space is separable iff it is second countable

Published on 01 Jul 2013 - 6:53

score 2.9k · Answer 4 · 2026-02-23 05:12:23

2.9k

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Confusion regarding the proof to "every Lindelöf metric space is second countable".

Published on 23 Feb 2026 - 5:12

score 1.6k · Answer 5 · 2013-07-09 19:30:43

1.6k

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locally compact Hausdorff space which is not second-countable

Published on 09 Jul 2013 - 19:30

score 5k · Answer 6 · 2013-07-31 11:53:24

5k

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Every locally compact, second countable Hausdorff space has a countable basis of open sets with compact closure

Published on 31 Jul 2013 - 11:53

score 4.9k · Answer 7 · 2013-11-19 21:43:36

4.9k

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Compact metric spaces is second countable and axiom of countable choice

Published on 19 Nov 2013 - 21:43

score 6.4k · Answer 8 · 2014-02-03 06:50:20

6.4k

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Prove that every compact metric space $K$ has a countable base, and that $K$ is therefore separable.

Published on 03 Feb 2014 - 6:50

score 110 · Answer 9 · 2017-04-18 18:15:22

110

Views

Why are manifolds second countable

Published on 18 Apr 2017 - 18:15

score 278 · Answer 10 · 2017-04-19 15:22:56

278

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Show that any countable subset of the reals is negligible

Published on 19 Apr 2017 - 15:22

score 4.3k · Answer 11 · 2017-04-29 14:41:09

4.3k

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If X is second-countable, then X is Lindelöf.

Published on 29 Apr 2017 - 14:41

score 64 · Answer 12 · 2017-05-12 00:53:23

64

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If $\sqcup_{i\in A} X_i$ is second countable and $X_i$ is second countable, then $A$ is countable. Is this true?

Published on 12 May 2017 - 0:53

score 949 · Answer 13 · 2017-05-17 00:17:02

949

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Second Countability Proof

Published on 17 May 2017 - 0:17

score 409 · Answer 14 · 2026-03-25 15:59:05

409

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basis of a second countable, topology

Published on 25 Mar 2026 - 15:59

score 119 · Answer 15 · 2017-07-05 16:08:15

119

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Countable and dense Baire subsets

Published on 05 Jul 2017 - 16:08

List Question

Properties of Infinite set on co-finite topology and Countable set on co-countable topology

$X$ second countable locally compact Hausdorff implies $C(X)$ separable?

A metric space is separable iff it is second countable

Confusion regarding the proof to "every Lindelöf metric space is second countable".

locally compact Hausdorff space which is not second-countable

Every locally compact, second countable Hausdorff space has a countable basis of open sets with compact closure

Compact metric spaces is second countable and axiom of countable choice

Prove that every compact metric space $K$ has a countable base, and that $K$ is therefore separable.

Why are manifolds second countable

Show that any countable subset of the reals is negligible

If X is second-countable, then X is Lindelöf.

If $\sqcup_{i\in A} X_i$ is second countable and $X_i$ is second countable, then $A$ is countable. Is this true?

Second Countability Proof

basis of a second countable, topology

Countable and dense Baire subsets

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