Question

Pathological examples of compact sets in analysis

score 345 · Answer 1 · 2026-04-11 14:16:16

345

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Pathological examples of compact sets in analysis

Published on 11 Apr 2026 - 14:16

score 438 · Answer 2 · 2026-04-17 05:52:19

438

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When we say that $\mathbb S^1$ is compact, which topology we are thinking about?

Published on 17 Apr 2026 - 5:52

score 44 · Answer 3 · 2026-05-15 05:30:11

44

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Uniform convergence of logarithm on a compact set.

Published on 15 May 2026 - 5:30

score 67 · Answer 4 · 2026-04-12 22:31:21

67

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Can ANY compact set in $\mathbb R$ (which is not closed and bounded interval and $\varnothing$) be written as $[a,b] - \bigcup\limits_{n} I_n$?

Published on 12 Apr 2026 - 22:31

score 995 · Answer 5 · 2026-05-11 08:42:45

995

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proof that $[0,1]$ is compact

Published on 11 May 2026 - 8:42

score 523 · Answer 6 · 2026-04-10 01:53:41

523

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Proof attempt at "Adjoint of compact operator is compact" on Banach spaces

Published on 10 Apr 2026 - 1:53

score 216 · Answer 7 · 2026-04-13 23:49:37

216

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X compact iff any collection of closed set closed by finite intersection have a nonempty intersection

Published on 13 Apr 2026 - 23:49

score 239 · Answer 8 · 2026-05-10 15:27:19

239

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Dual Character for Compact Lie Groups

Published on 10 May 2026 - 15:27

score 39 · Answer 9 · 2026-04-11 17:24:44

39

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Disconnected compact subsets of $\mathbb{R^{n}}$

Published on 11 Apr 2026 - 17:24

score 188 · Answer 10 · 2026-05-11 07:46:38

188

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Projective space, showing open map to one point compactification of $\Bbb C$

Published on 11 May 2026 - 7:46

score 134 · Answer 11 · 2026-04-14 05:19:20

134

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Family of Closed set of $X$ having finite intersection property with arbitary intersection is non empty Then $X$ is compact metric space

Published on 14 Apr 2026 - 5:19

score 169 · Answer 12 · 2026-05-10 12:53:22

169

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A Corollary from Munkres' Topology

Published on 10 May 2026 - 12:53

score 618 · Answer 13 · 2026-04-16 04:26:15

618

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Prob. 5, Sec. 26, in Munkres' TOPOLOGY, 2nd ed: Any pair of disjoint compact subspaces of a Hausdorff is separated by disjoint open sets

Published on 16 Apr 2026 - 4:26

score 605 · Answer 14 · 2026-05-15 05:31:38

605

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Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

Published on 15 May 2026 - 5:31

score 109 · Answer 15 · 2026-04-09 08:08:28

109

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A sequence of functions decreasing to 0 is equicontinuous in a compact metric space.

Published on 09 Apr 2026 - 8:08

List Question

Pathological examples of compact sets in analysis

When we say that $\mathbb S^1$ is compact, which topology we are thinking about?

Uniform convergence of logarithm on a compact set.

Can ANY compact set in $\mathbb R$ (which is not closed and bounded interval and $\varnothing$) be written as $[a,b] - \bigcup\limits_{n} I_n$?

proof that $[0,1]$ is compact

Proof attempt at "Adjoint of compact operator is compact" on Banach spaces

X compact iff any collection of closed set closed by finite intersection have a nonempty intersection

Dual Character for Compact Lie Groups

Disconnected compact subsets of $\mathbb{R^{n}}$

Projective space, showing open map to one point compactification of $\Bbb C$

Family of Closed set of $X$ having finite intersection property with arbitary intersection is non empty Then $X$ is compact metric space

A Corollary from Munkres' Topology

Prob. 5, Sec. 26, in Munkres' TOPOLOGY, 2nd ed: Any pair of disjoint compact subspaces of a Hausdorff is separated by disjoint open sets

Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

A sequence of functions decreasing to 0 is equicontinuous in a compact metric space.

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