Question

Compactness of $A \subset l^2(\mathbb{N})$

score 32 · Answer 1 · 2026-04-14 16:13:15

32

Views

Compactness of $A \subset l^2(\mathbb{N})$

Published on 14 Apr 2026 - 16:13

score 447 · Answer 2 · 2026-04-13 20:59:23

447

Views

The product of a function that vanishes at infinity and a continuous bounded one

Published on 13 Apr 2026 - 20:59

score 248 · Answer 3 · 2026-04-12 09:50:36

248

Views

$A$ compact $\implies$ $\overline{A}$ compact?

Published on 12 Apr 2026 - 9:50

score 565 · Answer 4 · 2026-04-12 05:36:02

Why is in the definition of the space of continuous functions vanishing at infinity from a space $Ω$ to $ℝ$, $Ω$ often assumed to be locally compact?

score 208 · Answer 5 · 2026-04-16 04:48:05

208

Views

Is the set $\{ x \in [0,1] | e^x \cos(\sqrt{x^2+1}) \leq 1 \}$ compact?

Published on 16 Apr 2026 - 4:48

score 92 · Answer 6 · 2026-04-15 04:12:10

92

Views

Show that $F = \{\lambda x|\lambda\in \mathbb{R}_+, x\in K\}$ is closed where $K$ is a compact set.

Published on 15 Apr 2026 - 4:12

score 1k · Answer 7 · 2026-04-11 07:25:43

1k

Views

Rudin's Proof of Bolzano-Weierstrass theorem

Published on 11 Apr 2026 - 7:25

score 4.7k · Answer 8 · 2026-04-16 15:09:10

4.7k

Views

Is $\Bbb Q$ intersect $[0,1]$ in $\Bbb R$ compact?

Published on 16 Apr 2026 - 15:09

score 393 · Answer 9 · 2026-05-10 19:03:12

393

Views

Certain Set of Functions with Bounded Variation is Compact

Published on 10 May 2026 - 19:03

score 886 · Answer 10 · 2026-05-10 22:28:49

886

Views

One point compactification is compact

Published on 10 May 2026 - 22:28

score 325 · Answer 11 · 2026-05-10 18:44:02

325

Views

For what spaces does every countable Borel cover have a finite subcover?

Published on 10 May 2026 - 18:44

score 177 · Answer 12 · 2026-04-13 15:30:14

177

Views

$(X,T)$ is compact iff every family of closed set ${F}_{i \in I}$ with non-empty finite intersections has an overall intersection that is not empty.

Published on 13 Apr 2026 - 15:30

score 25 · Answer 13 · 2026-04-13 05:37:57

25

Views

$D=\{z\in\mathbb{C}:|z|<1\}$. Every compact subset $K$ of D, $K \subseteq D$ is in $rD$ for sufficiently large $0\le r<1$

Published on 13 Apr 2026 - 5:37

score 60 · Answer 14 · 2026-04-15 17:57:35

60

Views

If $f_k \to f$ uniformly, then $J(f_k) \to J(f)$, where $J: \mathcal{C}_{\text{c}}(\mathbb{R}^d) \to \mathbb{R}$ ist linear and monotonous

Published on 15 Apr 2026 - 17:57

score 78 · Answer 15 · 2026-04-13 20:00:03

78

Views

Alexandroff One Point Compactification of $[0,1]\times[0,1)$

Published on 13 Apr 2026 - 20:00

List Question

Compactness of $A \subset l^2(\mathbb{N})$

The product of a function that vanishes at infinity and a continuous bounded one

$A$ compact $\implies$ $\overline{A}$ compact?

Why is in the definition of the space of continuous functions vanishing at infinity from a space $Ω$ to $ℝ$, $Ω$ often assumed to be locally compact?

Is the set $\{ x \in [0,1] | e^x \cos(\sqrt{x^2+1}) \leq 1 \}$ compact?

Show that $F = \{\lambda x|\lambda\in \mathbb{R}_+, x\in K\}$ is closed where $K$ is a compact set.

Rudin's Proof of Bolzano-Weierstrass theorem

Is $\Bbb Q$ intersect $[0,1]$ in $\Bbb R$ compact?

Certain Set of Functions with Bounded Variation is Compact

One point compactification is compact

For what spaces does every countable Borel cover have a finite subcover?

$(X,T)$ is compact iff every family of closed set ${F}_{i \in I}$ with non-empty finite intersections has an overall intersection that is not empty.

$D=\{z\in\mathbb{C}:|z|<1\}$. Every compact subset $K$ of D, $K \subseteq D$ is in $rD$ for sufficiently large $0\le r<1$

If $f_k \to f$ uniformly, then $J(f_k) \to J(f)$, where $J: \mathcal{C}_{\text{c}}(\mathbb{R}^d) \to \mathbb{R}$ ist linear and monotonous

Alexandroff One Point Compactification of $[0,1]\times[0,1)$

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