Question

Compactification of $\mathbb{C}^{n}$

score 79 · Answer 1 · 2026-03-28 01:47:24

79

Views

Compactification of $\mathbb{C}^{n}$

Published on 28 Mar 2026 - 1:47

score 413 · Answer 2 · 2019-02-21 05:06:53

413

Views

Expanding a compact subset of $\mathbb R^n$

Published on 21 Feb 2019 - 5:06

score 590 · Answer 3 · 2019-02-21 18:49:36

590

Views

A compact subset of a metric space is always closed

Published on 21 Feb 2019 - 18:49

score 78 · Answer 4 · 2026-03-25 23:38:12

78

Views

If $\|A(x)\|_Y \geq c \|x\|_X$ and $\dim X = + \infty$, can $A \in \mathcal{L}(X,Y)$ be a compact operator?

Published on 25 Mar 2026 - 23:38

score 76 · Answer 5 · 2026-03-30 04:54:50

76

Views

Is {-1,1}^N compact in $\ell_\infty$?

Published on 30 Mar 2026 - 4:54

score 643 · Answer 6 · 2019-02-23 17:27:49

643

Views

Proof of a compact set without using Heine-Borel

Published on 23 Feb 2019 - 17:27

score 30 · Answer 7 · 2026-03-25 17:42:22

30

Views

Showing that $0 \in \overline{A(\partial B_1^X)}$ if $X,Y$ Banach with $\dim X = + \infty$ and $A \in \mathcal{L}_c(X,Y)$.

Published on 25 Mar 2026 - 17:42

score 70 · Answer 8 · 2026-03-25 20:35:57

70

Views

Showing that $\exists x \in H : \|A(x)\| = \|A\|_\mathcal{L}$ if $H$ is Hilbert and $A \in \mathcal{L}_c(X,Y)$.

Published on 25 Mar 2026 - 20:35

score 422 · Answer 9 · 2019-02-24 11:05:30

422

Views

Example 2, Sec. 28, in Munkres' TOPOLOGY, 2nd ed.: Does every compact ordered (or well-ordered) set always have a largest element.

Published on 24 Feb 2019 - 11:05

score 84 · Answer 10 · 2019-02-25 16:14:48

84

Views

let $S=\{ \frac{1}{m}+\frac{1}{n}:m,n\in \mathbb{N}\} \cup \{0\}$. then $S$ is compact set in $\mathbb{R}$. True or False.

Published on 25 Feb 2019 - 16:14

score 70 · Answer 11 · 2019-02-25 18:00:08

70

Views

Does locally compact, not nowhere-dense topological subspace always contain open subset?

Published on 25 Feb 2019 - 18:00

score 32 · Answer 12 · 2026-03-29 23:48:14

32

Views

Show local uniform convergence for composition of continuous and affine map on compact set.

Published on 29 Mar 2026 - 23:48

score 192 · Answer 13 · 2026-03-29 23:45:27

192

Views

Convergence of suprema of sequence of functions

Published on 29 Mar 2026 - 23:45

score 142 · Answer 14 · 2026-03-30 00:04:01

142

Views

Understanding the term "Technical Machinery"

Published on 30 Mar 2026 - 0:04

score 175 · Answer 15 · 2019-02-28 08:18:56

175

Views

A countable product of many sequentially compact spaces is a sequentially compact space

Published on 28 Feb 2019 - 8:18

List Question

Compactification of $\mathbb{C}^{n}$

Expanding a compact subset of $\mathbb R^n$

A compact subset of a metric space is always closed

If $\|A(x)\|_Y \geq c \|x\|_X$ and $\dim X = + \infty$, can $A \in \mathcal{L}(X,Y)$ be a compact operator?

Is {-1,1}^N compact in $\ell_\infty$?

Proof of a compact set without using Heine-Borel

Showing that $0 \in \overline{A(\partial B_1^X)}$ if $X,Y$ Banach with $\dim X = + \infty$ and $A \in \mathcal{L}_c(X,Y)$.

Showing that $\exists x \in H : \|A(x)\| = \|A\|_\mathcal{L}$ if $H$ is Hilbert and $A \in \mathcal{L}_c(X,Y)$.

Example 2, Sec. 28, in Munkres' TOPOLOGY, 2nd ed.: Does every compact ordered (or well-ordered) set always have a largest element.

let $S=\{ \frac{1}{m}+\frac{1}{n}:m,n\in \mathbb{N}\} \cup \{0\}$. then $S$ is compact set in $\mathbb{R}$. True or False.

Does locally compact, not nowhere-dense topological subspace always contain open subset?

Show local uniform convergence for composition of continuous and affine map on compact set.

Convergence of suprema of sequence of functions

Understanding the term "Technical Machinery"

A countable product of many sequentially compact spaces is a sequentially compact space

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