Question

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

score 81 · Answer 1 · 2026-04-14 16:13:13

81

Views

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

Published on 14 Apr 2026 - 16:13

score 416 · Answer 2 · 2026-04-10 15:52:14

416

Views

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

Published on 10 Apr 2026 - 15:52

score 593 · Answer 3 · 2026-04-14 16:04:10

593

Views

A compact subset of a metric space is always closed

Published on 14 Apr 2026 - 16:04

score 81 · Answer 4 · 2026-05-13 23:34:42

81

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 13 May 2026 - 23:34

score 78 · Answer 5 · 2026-04-11 02:43:51

78

Views

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

Published on 11 Apr 2026 - 2:43

score 646 · Answer 6 · 2026-04-09 08:53:16

646

Views

Proof of a compact set without using Heine-Borel

Published on 09 Apr 2026 - 8:53

score 33 · Answer 7 · 2026-05-13 22:11:46

33

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 13 May 2026 - 22:11

score 73 · Answer 8 · 2026-05-13 22:10:04

73

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 13 May 2026 - 22:10

score 425 · Answer 9 · 2026-04-12 18:43:54

425

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 12 Apr 2026 - 18:43

score 87 · Answer 10 · 2026-04-16 04:59:38

87

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 16 Apr 2026 - 4:59

score 73 · Answer 11 · 2026-04-12 20:49:45

73

Views

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

Published on 12 Apr 2026 - 20:49

score 35 · Answer 12 · 2026-05-15 20:06:35

35

Views

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

Published on 15 May 2026 - 20:06

score 195 · Answer 13 · 2026-05-15 20:06:56

195

Views

Convergence of suprema of sequence of functions

Published on 15 May 2026 - 20:06

score 144 · Answer 14 · 2026-04-08 20:17:09

144

Views

Understanding the term "Technical Machinery"

Published on 08 Apr 2026 - 20:17

score 179 · Answer 15 · 2026-04-14 04:19:57

179

Views

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

Published on 14 Apr 2026 - 4:19

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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