Question

$H^2(\mathbb R^3 \setminus \{0\})$ does not vanish

score 216 · Answer 1 · 2026-03-25 06:24:29

216

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$H^2(\mathbb R^3 \setminus \{0\})$ does not vanish

Published on 25 Mar 2026 - 6:24

score 123 · Answer 2 · 2026-04-25 11:30:24

123

Views

Real Analysis: Determine Whether the Following Sets are Open in $E^1$, closed in $E^1$ or neither.

Published on 25 Apr 2026 - 11:30

score 1.2k · Answer 3 · 2026-04-16 04:08:40

1.2k

Views

Show that a sequence is not a Cauchy Sequence

Published on 16 Apr 2026 - 4:08

score 37 · Answer 4 · 2026-04-10 00:34:43

37

Views

Is it possible to have such kind of two functions?

Published on 10 Apr 2026 - 0:34

score 3.5k · Answer 5 · 2026-04-23 16:35:30

3.5k

Views

Understanding the Stone-Weierstrass Theorem in Rudin's Principle of Mathematical Analysis

Published on 23 Apr 2026 - 16:35

score 22 · Answer 6 · 2026-04-10 11:29:08

22

Views

Is a homomorphic function under addition even on $\mathbb{R}$?

Published on 10 Apr 2026 - 11:29

score 368 · Answer 7 · 2026-04-16 19:29:17

368

Views

How to prove this is a decreasing sequence?

Published on 16 Apr 2026 - 19:29

score 1.6k · Answer 8 · 2026-04-15 13:21:07

1.6k

Views

If $A$ is a closed set that contains every rational number $r\in [0,1]$, show that $[0,1]\subset A$

Published on 15 Apr 2026 - 13:21

score 150 · Answer 9 · 2026-04-14 06:05:38

150

Views

Multiplying two power series with negative indices

Published on 14 Apr 2026 - 6:05

score 82 · Answer 10 · 2026-04-16 10:59:42

82

Views

Is $\sum_{n=0}^\infty \int_0^1 \frac{\cos\left(n\pi x\right)}{\log\log\frac{4}{x}}dx$ is divergent or not?

Published on 16 Apr 2026 - 10:59

score 86 · Answer 11 · 2026-04-10 18:13:35

86

Views

A question about to infimum and Supermum on a bounded set

Published on 10 Apr 2026 - 18:13

score 1.6k · Answer 12 · 2026-04-11 23:46:26

1.6k

Views

How to prove $f(z)=|z|$ is continuous?

Published on 11 Apr 2026 - 23:46

score 86 · Answer 13 · 2026-04-12 12:19:41

86

Views

How to prove that $f:X\to Y$ can be extended to a continuous function on $\overline{X}$

Published on 12 Apr 2026 - 12:19

score 83 · Answer 14 · 2026-04-16 22:43:37

83

Views

Elementary proof for $\lim_{n\to \infty}\sqrt[2n-1]{\dfrac{1}{2^n}}=\dfrac1{\sqrt 2}$

Published on 16 Apr 2026 - 22:43

score 63 · Answer 15 · 2026-04-16 15:10:13

63

Views

Prove that there are $0<c<\frac{\pi }{2}$ such that $f'(c)=(f(\frac{\pi }{2})-f(0))\cos (c)$

Published on 16 Apr 2026 - 15:10

List Question

$H^2(\mathbb R^3 \setminus \{0\})$ does not vanish

Real Analysis: Determine Whether the Following Sets are Open in $E^1$, closed in $E^1$ or neither.

Show that a sequence is not a Cauchy Sequence

Is it possible to have such kind of two functions?

Understanding the Stone-Weierstrass Theorem in Rudin's Principle of Mathematical Analysis

Is a homomorphic function under addition even on $\mathbb{R}$?

How to prove this is a decreasing sequence?

If $A$ is a closed set that contains every rational number $r\in [0,1]$, show that $[0,1]\subset A$

Multiplying two power series with negative indices

Is $\sum_{n=0}^\infty \int_0^1 \frac{\cos\left(n\pi x\right)}{\log\log\frac{4}{x}}dx$ is divergent or not?

A question about to infimum and Supermum on a bounded set

How to prove $f(z)=|z|$ is continuous?

How to prove that $f:X\to Y$ can be extended to a continuous function on $\overline{X}$

Elementary proof for $\lim_{n\to \infty}\sqrt[2n-1]{\dfrac{1}{2^n}}=\dfrac1{\sqrt 2}$

Prove that there are $0<c<\frac{\pi }{2}$ such that $f'(c)=(f(\frac{\pi }{2})-f(0))\cos (c)$

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