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Proof of Tychonoff's Theorem for an undergrad

score 1.7k · Answer 1 · 2026-04-10 06:13:21

1.7k

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Proof of Tychonoff's Theorem for an undergrad

Published on 10 Apr 2026 - 6:13

score 81 · Answer 2 · 2026-04-12 12:30:40

81

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Equivalence of precompactness and completely boundedness.

Published on 12 Apr 2026 - 12:30

score 653 · Answer 3 · 2026-04-15 19:54:51

653

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The proof of $[0,1] \cap \mathbb{Q}$ is totally bounded

Published on 15 Apr 2026 - 19:54

score 141 · Answer 4 · 2026-04-16 15:08:51

141

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is $[0,1]\backslash \mathbb{Q}$ totally bounded?

Published on 16 Apr 2026 - 15:08

score 3.5k · Answer 5 · 2026-04-11 00:45:55

3.5k

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The standard n-simplex is compact set

Published on 11 Apr 2026 - 0:45

score 10k · Answer 6 · 2026-04-15 15:05:51

10k

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Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?

Published on 15 Apr 2026 - 15:05

score 186 · Answer 7 · 2026-04-08 20:36:20

186

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Intiution behind the theorem about locally compact Hausdorff spaces

Published on 08 Apr 2026 - 20:36

score 165 · Answer 8 · 2026-04-20 14:29:24

165

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Proof that $C(K)$ is a Grothendieck space for $K$ an extremely disconnected compact space.

Published on 20 Apr 2026 - 14:29

score 149 · Answer 9 · 2026-04-17 13:07:13

149

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Under what condition a normal space is compact hausdorff?

Published on 17 Apr 2026 - 13:07

score 234 · Answer 10 · 2026-04-16 04:47:22

234

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For compact Lie groups, is $[\mathfrak{g},\mathfrak{g}]=\mathfrak{g}$ equivalent to being semisimple?

Published on 16 Apr 2026 - 4:47

score 2.7k · Answer 11 · 2026-03-29 14:20:10

2.7k

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Prove $\lim \sup f (x_n) = f(\lim \sup (x_n)) $ and same for $\inf$

Published on 29 Mar 2026 - 14:20

score 225 · Answer 12 · 2026-04-11 15:20:28

225

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If $X \cup \{\infty\}$ is compact, then $X$ is locally compact?

Published on 11 Apr 2026 - 15:20

score 491 · Answer 13 · 2026-04-09 16:29:30

491

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Prove that a metrizable space is countably compact iff it is compact.

Published on 09 Apr 2026 - 16:29

score 102 · Answer 14 · 2026-04-13 14:00:52

102

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Stone–Čech compactification equivalence

Published on 13 Apr 2026 - 14:00

score 2.6k · Answer 15 · 2026-04-14 07:39:26

2.6k

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A topological space is countably compact iff every countably infinite subset has a limit point

Published on 14 Apr 2026 - 7:39

List Question

Proof of Tychonoff's Theorem for an undergrad

Equivalence of precompactness and completely boundedness.

The proof of $[0,1] \cap \mathbb{Q}$ is totally bounded

is $[0,1]\backslash \mathbb{Q}$ totally bounded?

The standard n-simplex is compact set

Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?

Intiution behind the theorem about locally compact Hausdorff spaces

Proof that $C(K)$ is a Grothendieck space for $K$ an extremely disconnected compact space.

Under what condition a normal space is compact hausdorff?

For compact Lie groups, is $[\mathfrak{g},\mathfrak{g}]=\mathfrak{g}$ equivalent to being semisimple?

Prove $\lim \sup f (x_n) = f(\lim \sup (x_n)) $ and same for $\inf$

If $X \cup \{\infty\}$ is compact, then $X$ is locally compact?

Prove that a metrizable space is countably compact iff it is compact.

Stone–Čech compactification equivalence

A topological space is countably compact iff every countably infinite subset has a limit point

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