Question

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

score 31 · Answer 1 · 2026-03-29 05:11:50

31

Views

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

Published on 29 Mar 2026 - 5:11

score 444 · Answer 2 · 2018-11-06 17:40:43

444

Views

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

Published on 06 Nov 2018 - 17:40

score 245 · Answer 3 · 2018-11-06 22:50:37

245

Views

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

Published on 06 Nov 2018 - 22:50

score 562 · Answer 4 · 2018-11-07 12:38:55

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 205 · Answer 5 · 2018-11-07 18:40:22

205

Views

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

Published on 07 Nov 2018 - 18:40

score 89 · Answer 6 · 2018-11-07 22:08:06

89

Views

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

Published on 07 Nov 2018 - 22:08

score 1k · Answer 7 · 2018-11-08 06:00:58

1k

Views

Rudin's Proof of Bolzano-Weierstrass theorem

Published on 08 Nov 2018 - 6:00

score 4.7k · Answer 8 · 2018-11-08 15:39:45

4.7k

Views

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

Published on 08 Nov 2018 - 15:39

score 390 · Answer 9 · 2026-03-25 17:37:17

390

Views

Certain Set of Functions with Bounded Variation is Compact

Published on 25 Mar 2026 - 17:37

score 885 · Answer 10 · 2026-03-27 07:16:48

885

Views

One point compactification is compact

Published on 27 Mar 2026 - 7:16

score 322 · Answer 11 · 2026-03-25 09:12:26

322

Views

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

Published on 25 Mar 2026 - 9:12

score 175 · Answer 12 · 2026-03-27 13:48:25

175

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 27 Mar 2026 - 13:48

score 22 · Answer 13 · 2018-11-11 12:16:19

22

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 11 Nov 2018 - 12:16

score 57 · Answer 14 · 2018-11-12 19:31:17

57

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 12 Nov 2018 - 19:31

score 75 · Answer 15 · 2018-11-13 17:03:37

75

Views

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

Published on 13 Nov 2018 - 17:03

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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