Question

Show that the set $C := \left\{\left.\sum_{j=1}^\infty\lambda_j e_j\right|\, \lambda_j \in \mathbb{K},\,|\lambda_j| \leq a_j\right\}$ is compact in H.

score 115 · Answer 1 · 2023-11-15 10:18:29

115

Views

Show that the set $C := \left\{\left.\sum_{j=1}^\infty\lambda_j e_j\right|\, \lambda_j \in \mathbb{K},\,|\lambda_j| \leq a_j\right\}$ is compact in H.

Published on 15 Nov 2023 - 10:18

score 168 · Answer 2 · 2026-04-10 10:17:18

168

Views

Compact and connected in quotient space

Published on 10 Apr 2026 - 10:17

score 31 · Answer 3 · 2026-03-29 15:59:58

31

Views

Characterization by nets of relatively countable compact set on TVS

Published on 29 Mar 2026 - 15:59

score 64 · Answer 4 · 2026-04-11 08:58:48

64

Views

The topology of a compact Hausdorff space $X$ is precisely the weak topology due to $C(X)$. How?

Published on 11 Apr 2026 - 8:58

score 95 · Answer 5 · 2023-11-18 08:04:00

95

Views

Rudin Real Analysis exercise 2.13, question about last part.

Published on 18 Nov 2023 - 8:04

score 117 · Answer 6 · 2023-11-18 10:15:24

117

Views

Proof that pointwise continuity implies uniform continuity for functions on compact sets

Published on 18 Nov 2023 - 10:15

score 40 · Answer 7 · 2026-04-07 18:11:13

40

Views

Inlcusion of compactly supported Sobolev Space in Closure of $C_0^{\infty}\left(\mathbb{R}^n\right)$ in $W^{k,q}(\Omega)$

Published on 07 Apr 2026 - 18:11

score 129 · Answer 8 · 2023-11-21 11:25:08

129

Views

Compactness in angelic spaces

Published on 21 Nov 2023 - 11:25

score 86 · Answer 9 · 2023-11-26 00:11:51

86

Views

Munkres section 26 problem 2- Open coverings

Published on 26 Nov 2023 - 0:11

score 107 · Answer 10 · 2023-11-27 02:15:28

107

Views

Where is the property "the intersection of compacts is compact" positioned among the lower separation axioms?

Published on 27 Nov 2023 - 2:15

score 61 · Answer 11 · 2026-04-11 09:33:25

61

Views

Show that the unit sphere in the space of continuous functions $\mathcal{C}_p^0[0,1]$ is not compact

Published on 11 Apr 2026 - 9:33

score 48 · Answer 12 · 2023-11-29 12:33:04

48

Views

Prove that $\cup_{p \in M} \overline{B}(p, r)$ is compact

Published on 29 Nov 2023 - 12:33

score 35 · Answer 13 · 2026-03-29 15:16:40

35

Views

X/A with respect to the quotient topology is Hausdorff?

Published on 29 Mar 2026 - 15:16

score 38 · Answer 14 · 2023-11-29 18:04:02

38

Views

Given any compact set in $\mathbb{R}^n$, the closure of the interior of the set is also compact.

Published on 29 Nov 2023 - 18:04

score 36 · Answer 15 · 2026-04-09 19:45:12

36

Views

Compactness criterion for subsets in a fractional sobolev space

Published on 09 Apr 2026 - 19:45

List Question

Show that the set $C := \left\{\left.\sum_{j=1}^\infty\lambda_j e_j\right|\, \lambda_j \in \mathbb{K},\,|\lambda_j| \leq a_j\right\}$ is compact in H.

Compact and connected in quotient space

Characterization by nets of relatively countable compact set on TVS

The topology of a compact Hausdorff space $X$ is precisely the weak topology due to $C(X)$. How?

Rudin Real Analysis exercise 2.13, question about last part.

Proof that pointwise continuity implies uniform continuity for functions on compact sets

Inlcusion of compactly supported Sobolev Space in Closure of $C_0^{\infty}\left(\mathbb{R}^n\right)$ in $W^{k,q}(\Omega)$

Compactness in angelic spaces

Munkres section 26 problem 2- Open coverings

Where is the property "the intersection of compacts is compact" positioned among the lower separation axioms?

Show that the unit sphere in the space of continuous functions $\mathcal{C}_p^0[0,1]$ is not compact

Prove that $\cup_{p \in M} \overline{B}(p, r)$ is compact

X/A with respect to the quotient topology is Hausdorff?

Given any compact set in $\mathbb{R}^n$, the closure of the interior of the set is also compact.

Compactness criterion for subsets in a fractional sobolev space

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