Question

if arbitrary intersection of compact sets is empty, then there exists at least two sets that are disjoint?

score 151 · Answer 1 · 2016-10-19 21:11:30

151

Views

if arbitrary intersection of compact sets is empty, then there exists at least two sets that are disjoint?

Published on 19 Oct 2016 - 21:11

score 19k · Answer 2 · 2016-10-20 06:05:46

19k

Views

prove that any finite set in a metric space is compact

Published on 20 Oct 2016 - 6:05

score 79 · Answer 3 · 2016-10-20 08:30:42

79

Views

Weak compactness in Kreps-Yan theorem

Published on 20 Oct 2016 - 8:30

score 178 · Answer 4 · 2016-10-21 12:03:40

178

Views

Infinite-dimensional subspace of a Hilbert space

Published on 21 Oct 2016 - 12:03

score 54 · Answer 5 · 2016-10-22 09:10:27

54

Views

The set of compact open subsets of a compact set is a $\sigma$-algebra?

Published on 22 Oct 2016 - 9:10

score 309 · Answer 6 · 2016-10-22 14:50:30

309

Views

Every infinite subset $E$ of a compact set $K$ contains a limit point in $K$

Published on 22 Oct 2016 - 14:50

score 774 · Answer 7 · 2026-02-23 12:02:51

774

Views

A sequence that is uniformly bounded on a compact interval is equicontinuous

Published on 23 Feb 2026 - 12:02

score 52 · Answer 8 · 2026-03-30 05:32:12

52

Views

Reverse of the statement of uniform continuity on a compact

Published on 30 Mar 2026 - 5:32

score 670 · Answer 9 · 2016-10-24 00:28:31

670

Views

Compactness of the integral operator $(Bf)(t)=\int_0^\infty\alpha (t,s)f(s)ds$

Published on 24 Oct 2016 - 0:28

score 357 · Answer 10 · 2016-10-25 05:47:36

357

Views

Proving distance between bounded and compact set in $\mathbb{R}$

Published on 25 Oct 2016 - 5:47

score 543 · Answer 11 · 2016-10-25 06:57:06

543

Views

Must every bounded nonempty set in $\Bbb R^n$ have a non empty boundary?

Published on 25 Oct 2016 - 6:57

score 1.3k · Answer 12 · 2026-03-26 06:07:02

1.3k

Views

Proving that if $A$ and $B$ are compact spaces, then $A\times B$ is compact

Published on 26 Mar 2026 - 6:07

score 387 · Answer 13 · 2016-10-25 19:12:39

387

Views

Where is topological input needed in "compact iff every net has an accumulation point"?

Published on 25 Oct 2016 - 19:12

score 106 · Answer 14 · 2016-10-26 05:32:32

106

Views

Given $E=\{ p_n : n \in \mathbb{N}$ and $lim_{n\rightarrow \infty} p_n =p\}$. Prove $Cl(E)=E \cup\{p\}$ and $Cl(E)$ is compact

Published on 26 Oct 2016 - 5:32

score 467 · Answer 15 · 2016-10-26 19:45:31

467

Views

The union of finitely many compact subsets of $\mathbb{R}^n$ must be compact.

Published on 26 Oct 2016 - 19:45

List Question

if arbitrary intersection of compact sets is empty, then there exists at least two sets that are disjoint?

prove that any finite set in a metric space is compact

Weak compactness in Kreps-Yan theorem

Infinite-dimensional subspace of a Hilbert space

The set of compact open subsets of a compact set is a $\sigma$-algebra?

Every infinite subset $E$ of a compact set $K$ contains a limit point in $K$

A sequence that is uniformly bounded on a compact interval is equicontinuous

Reverse of the statement of uniform continuity on a compact

Compactness of the integral operator $(Bf)(t)=\int_0^\infty\alpha (t,s)f(s)ds$

Proving distance between bounded and compact set in $\mathbb{R}$

Must every bounded nonempty set in $\Bbb R^n$ have a non empty boundary?

Proving that if $A$ and $B$ are compact spaces, then $A\times B$ is compact

Where is topological input needed in "compact iff every net has an accumulation point"?

Given $E=\{ p_n : n \in \mathbb{N}$ and $lim_{n\rightarrow \infty} p_n =p\}$. Prove $Cl(E)=E \cup\{p\}$ and $Cl(E)$ is compact

The union of finitely many compact subsets of $\mathbb{R}^n$ must be compact.

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