Question

Alternative proof: Metric space is compact iff it's sequentially compact.

score 61 · Answer 1 · 2026-04-09 18:55:29

61

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Alternative proof: Metric space is compact iff it's sequentially compact.

Published on 09 Apr 2026 - 18:55

score 69 · Answer 2 · 2026-04-12 07:14:19

69

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Show that $C_c(\mathbb{R})$ is a linear space.

Published on 12 Apr 2026 - 7:14

score 108 · Answer 3 · 2026-04-15 17:31:38

108

Views

Let $(X, \mathcal{T})$ and $(Y, \mathcal{U})$ be topological spaces. Show that $X \times Y \simeq Y\times X$

Published on 15 Apr 2026 - 17:31

score 63 · Answer 4 · 2026-04-13 17:12:31

63

Views

If $X$ is compact Hausdorf and $A$ is closed than $Y=A^c$ is locally compact

Published on 13 Apr 2026 - 17:12

score 92 · Answer 5 · 2026-04-15 17:41:13

92

Views

Show that $\operatorname{int}{(A \times B)} = \operatorname{int}(A) \times \operatorname{int}(B)$

Published on 15 Apr 2026 - 17:41

score 87 · Answer 6 · 2026-04-14 08:36:36

87

Views

3.6.10 Tao Analysis, need help wth checking my proof and seeking any advice for the proof-writing itself.

Published on 14 Apr 2026 - 8:36

score 103 · Answer 7 · 2026-04-16 15:18:01

103

Views

Proving the identity $\sum_{k=0}^{m} \binom{n-k}{m-k}= \binom{n+1}{m}$ .

Published on 16 Apr 2026 - 15:18

score 51 · Answer 8 · 2026-04-17 03:30:36

51

Views

Anagrams of STRAPAZZATA ending with A, and also starting and ending with A

Published on 17 Apr 2026 - 3:30

score 64 · Answer 9 · 2026-05-15 16:07:40

64

Views

Brezis' exercise 6.12: $\forall \varepsilon>0\,\exists C_\varepsilon > 0$ s.t. $\|u\|_\infty \le\varepsilon \|u'\|_\infty + C_\varepsilon \|u\|_{L^1}$

Published on 15 May 2026 - 16:07

score 127 · Answer 10 · 2026-05-15 16:07:41

127

Views

Brezis' exercise 6.12: a lemma of J.-L. Lions

Published on 15 May 2026 - 16:07

score 323 · Answer 11 · 2026-04-17 11:08:32

323

Views

Find the radius and the interval of convergence of the series $\sum_{n=1}^{\infty}\frac{n^3}{(n^2+1)^2}\left(\frac{4x-3}{x}\right)^n$.

Published on 17 Apr 2026 - 11:08

score 286 · Answer 12 · 2026-04-15 17:25:34

286

Views

Let $a$ and $b$ be rationals. Prove that if $a<b$ then there exists an irrational $x$ such that $a<x<b$.

Published on 15 Apr 2026 - 17:25

score 43 · Answer 13 · 2026-05-10 19:51:28

43

Views

Prove that the following properties are all finitely productive

Published on 10 May 2026 - 19:51

score 136 · Answer 14 · 2026-04-15 05:40:54

136

Views

Proving that $\lim_{n\to\infty} \frac{\text{cos}(n)+\text{sin}(n)}{n^2}=0$ using the definition of the limit

Published on 15 Apr 2026 - 5:40

score 61 · Answer 15 · 2026-04-16 11:52:55

61

Views

Prove explicitly that $\mathbb{R}^2_\text{usual} = (\mathbb{R}_\text{usual})^2$

Published on 16 Apr 2026 - 11:52

List Question

Alternative proof: Metric space is compact iff it's sequentially compact.

Show that $C_c(\mathbb{R})$ is a linear space.

Let $(X, \mathcal{T})$ and $(Y, \mathcal{U})$ be topological spaces. Show that $X \times Y \simeq Y\times X$

If $X$ is compact Hausdorf and $A$ is closed than $Y=A^c$ is locally compact

Show that $\operatorname{int}{(A \times B)} = \operatorname{int}(A) \times \operatorname{int}(B)$

3.6.10 Tao Analysis, need help wth checking my proof and seeking any advice for the proof-writing itself.

Proving the identity $\sum_{k=0}^{m} \binom{n-k}{m-k}= \binom{n+1}{m}$ .

Anagrams of STRAPAZZATA ending with A, and also starting and ending with A

Brezis' exercise 6.12: $\forall \varepsilon>0\,\exists C_\varepsilon > 0$ s.t. $\|u\|_\infty \le\varepsilon \|u'\|_\infty + C_\varepsilon \|u\|_{L^1}$

Brezis' exercise 6.12: a lemma of J.-L. Lions

Find the radius and the interval of convergence of the series $\sum_{n=1}^{\infty}\frac{n^3}{(n^2+1)^2}\left(\frac{4x-3}{x}\right)^n$.

Let $a$ and $b$ be rationals. Prove that if $a<b$ then there exists an irrational $x$ such that $a<x<b$.

Prove that the following properties are all finitely productive

Proving that $\lim_{n\to\infty} \frac{\text{cos}(n)+\text{sin}(n)}{n^2}=0$ using the definition of the limit

Prove explicitly that $\mathbb{R}^2_\text{usual} = (\mathbb{R}_\text{usual})^2$

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