Question

$X=\{(x,y)\mid x = r\cos(\frac{\pi}{2^n}), y = r\sin(\frac{\pi}{2^n}), 0\leq r\leq1, n = 2,3,4, \ldots\}$ $\cup \{(0,1)\}$ with the usual topology.

score 35 · Answer 1 · 2026-03-27 00:05:51

35

Views

$X=\{(x,y)\mid x = r\cos(\frac{\pi}{2^n}), y = r\sin(\frac{\pi}{2^n}), 0\leq r\leq1, n = 2,3,4, \ldots\}$ $\cup \{(0,1)\}$ with the usual topology.

Published on 27 Mar 2026 - 0:05

score 141 · Answer 2 · 2026-03-28 10:16:46

141

Views

Is the Lebesgue Measure on $[a,b]$ perfect?

Published on 28 Mar 2026 - 10:16

score 863 · Answer 3 · 2026-04-01 13:42:47

863

Views

Example of a sigma compact space which is not locally compact

Published on 01 Apr 2026 - 13:42

score 86 · Answer 4 · 2026-03-25 07:42:09

86

Views

Is every compact subset of a second countable space closed?

Published on 25 Mar 2026 - 7:42

score 567 · Answer 5 · 2026-03-25 07:42:48

567

Views

How can I prove that compact subset iff sequentially compact in second countable topological spaces?

Published on 25 Mar 2026 - 7:42

score 202 · Answer 6 · 2020-01-21 22:45:20

202

Views

Surjective function in topology

Published on 21 Jan 2020 - 22:45

score 657 · Answer 7 · 2026-04-01 15:01:14

657

Views

Can open balls of uniform radius around every point of a compact set $S$ be contained in an open set $U$ containing $S$?

Published on 01 Apr 2026 - 15:01

score 170 · Answer 8 · 2020-01-22 22:20:26

170

Views

compactness in $\ell^p$ space

Published on 22 Jan 2020 - 22:20

score 284 · Answer 9 · 2020-01-24 18:15:35

284

Views

Local compactness of the space of positive measures

Published on 24 Jan 2020 - 18:15

score 34 · Answer 10 · 2026-02-23 06:55:38

34

Views

Compactness results in $C^{k}(\Omega)$

Published on 23 Feb 2026 - 6:55

score 146 · Answer 11 · 2026-03-25 10:57:14

146

Views

Is a positive regular Borel measure on a compact Hausdorff space always finite?

Published on 25 Mar 2026 - 10:57

score 66 · Answer 12 · 2026-03-25 14:23:52

66

Views

Intersection of Powers of a Contraction Map is a Single Point

Published on 25 Mar 2026 - 14:23

score 500 · Answer 13 · 2020-01-30 11:35:51

500

Views

Every compact Hausdorff space can be expressed as a disjoint union of finitely many open sets.

Published on 30 Jan 2020 - 11:35

score 751 · Answer 14 · 2026-03-25 07:47:12

751

Views

Second countable and sequentially compact topological spaces are compact. Proof

Published on 25 Mar 2026 - 7:47

score 128 · Answer 15 · 2026-03-25 11:13:45

128

Views

Which one of the following implies the other?

Published on 25 Mar 2026 - 11:13

List Question

$X=\{(x,y)\mid x = r\cos(\frac{\pi}{2^n}), y = r\sin(\frac{\pi}{2^n}), 0\leq r\leq1, n = 2,3,4, \ldots\}$ $\cup \{(0,1)\}$ with the usual topology.

Is the Lebesgue Measure on $[a,b]$ perfect?

Example of a sigma compact space which is not locally compact

Is every compact subset of a second countable space closed?

How can I prove that compact subset iff sequentially compact in second countable topological spaces?

Surjective function in topology

Can open balls of uniform radius around every point of a compact set $S$ be contained in an open set $U$ containing $S$?

compactness in $\ell^p$ space

Local compactness of the space of positive measures

Compactness results in $C^{k}(\Omega)$

Is a positive regular Borel measure on a compact Hausdorff space always finite?

Intersection of Powers of a Contraction Map is a Single Point

Every compact Hausdorff space can be expressed as a disjoint union of finitely many open sets.

Second countable and sequentially compact topological spaces are compact. Proof

Which one of the following implies the other?

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