Question

Need for countable compactness in this proof for metric space convergence?

score 24 · Answer 1 · 2016-11-06 16:47:35

24

Views

Need for countable compactness in this proof for metric space convergence?

Published on 06 Nov 2016 - 16:47

score 370 · Answer 2 · 2026-03-26 09:35:47

370

Views

Every $\sigma$-compact LCH space is para-compact

Published on 26 Mar 2026 - 9:35

score 936 · Answer 3 · 2026-03-25 20:52:05

936

Views

Counterexample to the intersection of compact sets being compact.

Published on 25 Mar 2026 - 20:52

score 113 · Answer 4 · 2016-11-10 02:38:04

113

Views

How to use compact property to show this proof from topology

Published on 10 Nov 2016 - 2:38

score 312 · Answer 5 · 2026-04-02 11:15:14

312

Views

X is locally connected iff there is a finite cover of X by compact connected sets

Published on 02 Apr 2026 - 11:15

score 350 · Answer 6 · 2026-03-27 00:42:49

350

Views

Cartesian product of Cantor set is compact

Published on 27 Mar 2026 - 0:42

score 30 · Answer 7 · 2026-03-27 02:24:46

30

Views

There is a closest point $x\in C\times C$ ($C$ is the Cantor set) to $y\in C^c$

Published on 27 Mar 2026 - 2:24

score 200 · Answer 8 · 2016-11-11 04:30:55

200

Views

Show that unions of circles and $(0,0)$ is compact

Published on 11 Nov 2016 - 4:30

score 50 · Answer 9 · 2016-11-13 08:59:40

50

Views

If $X$ is a pseudocompact space and $Y$ is a second countable space then every continuous surjective map $f: X \to Y$ is $\mathbb{R}$-quotient

Published on 13 Nov 2016 - 8:59

score 743 · Answer 10 · 2016-11-15 00:05:04

743

Views

Proving $E= \{ \frac{1}{n^2} : n \in \mathbb{N} \} \cup \{0\}$ is compact

Published on 15 Nov 2016 - 0:05

score 532 · Answer 11 · 2016-11-15 06:03:30

532

Views

Let $f$ be usc and less than +$\infty$ on a compact set $E$ , show that $f$ assumes its maximum on E.

Published on 15 Nov 2016 - 6:03

score 127 · Answer 12 · 2026-03-29 06:07:57

127

Views

Use Compactness Theorem to prove that "an even number of things with property Y" cannot be expressed in first order predicate logic

Published on 29 Mar 2026 - 6:07

score 11.2k · Answer 13 · 2016-11-16 17:45:03

11.2k

Views

Is the convex hull of a compact set compact?

Published on 16 Nov 2016 - 17:45

score 113 · Answer 14 · 2016-11-16 18:36:01

113

Views

Prove/Disprove that $X$ is compact

Published on 16 Nov 2016 - 18:36

score 374 · Answer 15 · 2026-03-25 13:52:53

374

Views

Does every compact metric space have a finite basis?

Published on 25 Mar 2026 - 13:52

List Question

Need for countable compactness in this proof for metric space convergence?

Every $\sigma$-compact LCH space is para-compact

Counterexample to the intersection of compact sets being compact.

How to use compact property to show this proof from topology

X is locally connected iff there is a finite cover of X by compact connected sets

Cartesian product of Cantor set is compact

There is a closest point $x\in C\times C$ ($C$ is the Cantor set) to $y\in C^c$

Show that unions of circles and $(0,0)$ is compact

If $X$ is a pseudocompact space and $Y$ is a second countable space then every continuous surjective map $f: X \to Y$ is $\mathbb{R}$-quotient

Proving $E= \{ \frac{1}{n^2} : n \in \mathbb{N} \} \cup \{0\}$ is compact

Let $f$ be usc and less than +$\infty$ on a compact set $E$ , show that $f$ assumes its maximum on E.

Use Compactness Theorem to prove that "an even number of things with property Y" cannot be expressed in first order predicate logic

Is the convex hull of a compact set compact?

Prove/Disprove that $X$ is compact

Does every compact metric space have a finite basis?

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