Question

Can an open ball be a closed set and cannot be interpreted as a closed ball at the same time?

score 204 · Answer 1 · 2026-04-13 01:15:17

204

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Can an open ball be a closed set and cannot be interpreted as a closed ball at the same time?

Published on 13 Apr 2026 - 1:15

score 1.7k · Answer 2 · 2026-04-16 21:03:27

1.7k

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If $f_n\to f$ pointwise on $\mathbb{R}$ and each $f_n$ is bounded, then $f$ is bounded (counter-example) + question on uniform convergence proof

Published on 16 Apr 2026 - 21:03

score 106 · Answer 3 · 2026-04-10 15:30:08

106

Views

Composition of uniformly continuous functions

Published on 10 Apr 2026 - 15:30

score 104 · Answer 4 · 2026-05-04 09:02:51

104

Views

for $abs(Re(z))>\frac{1}{3}$ : $ Sign( Re(f(a+bi))) = Sign( Re(a)) $?

Published on 04 May 2026 - 9:02

score 204 · Answer 5 · 2026-04-16 20:44:15

204

Views

Counter examples on uniform convergence

Published on 16 Apr 2026 - 20:44

score 35 · Answer 6 · 2026-04-16 15:55:28

35

Views

Suppose that an $n \times n$ matrix has only real eigenvalues. Then $A$ is diagonalizable if and only if the dimension..

Published on 16 Apr 2026 - 15:55

score 185 · Answer 7 · 2026-04-16 06:07:28

185

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If $ x_{n}$ is unbounded sequence then the $\lim_{n \to \infty}\sin(\frac{1}{x_{n}})=0$

Published on 16 Apr 2026 - 6:07

score 201 · Answer 8 · 2026-04-13 21:53:36

201

Views

Convex/Concave functions composition counter-examples

Published on 13 Apr 2026 - 21:53

score 111 · Answer 9 · 2026-04-09 08:07:54

111

Views

Local Contractibility of Homogeneous, Locally Path-Connected Spaces

Published on 09 Apr 2026 - 8:07

score 47 · Answer 10 · 2026-04-14 18:58:41

47

Views

Can I conclude from $\sum_{n=1}^\infty u_n$ being convergent that $\sum_{n=1}^\infty (-1)^n\frac{u_n}{n}$ is convergent?

Published on 14 Apr 2026 - 18:58

score 92 · Answer 11 · 2026-04-16 15:53:33

92

Views

Proof or counterexample to $ \int_a^t |f(x)|dx \leq \sup_t|\int f(x)dx| $

Published on 16 Apr 2026 - 15:53

score 75 · Answer 12 · 2026-04-15 14:47:47

75

Views

Why is only assuming $\mathfrak g$ is nilpotent as a Lie algebra not sufficient for Engel's theorem?

Published on 15 Apr 2026 - 14:47

score 280 · Answer 13 · 2026-04-23 22:57:31

280

Views

Approximating Heaviside function by twice differentiable, monotone sequence

Published on 23 Apr 2026 - 22:57

score 75 · Answer 14 · 2026-04-14 03:26:29

75

Views

Non-isomorphic groups with same number of homomorphisms

Published on 14 Apr 2026 - 3:26

score 100 · Answer 15 · 2026-04-11 03:50:58

100

Views

Does the Image of a Loop under Contraction contain a Disc?

Published on 11 Apr 2026 - 3:50

List Question

Can an open ball be a closed set and cannot be interpreted as a closed ball at the same time?

If $f_n\to f$ pointwise on $\mathbb{R}$ and each $f_n$ is bounded, then $f$ is bounded (counter-example) + question on uniform convergence proof

Composition of uniformly continuous functions

for $abs(Re(z))>\frac{1}{3}$ : $ Sign( Re(f(a+bi))) = Sign( Re(a)) $?

Counter examples on uniform convergence

Suppose that an $n \times n$ matrix has only real eigenvalues. Then $A$ is diagonalizable if and only if the dimension..

If $ x_{n}$ is unbounded sequence then the $\lim_{n \to \infty}\sin(\frac{1}{x_{n}})=0$

Convex/Concave functions composition counter-examples

Local Contractibility of Homogeneous, Locally Path-Connected Spaces

Can I conclude from $\sum_{n=1}^\infty u_n$ being convergent that $\sum_{n=1}^\infty (-1)^n\frac{u_n}{n}$ is convergent?

Proof or counterexample to $ \int_a^t |f(x)|dx \leq \sup_t|\int f(x)dx| $

Why is only assuming $\mathfrak g$ is nilpotent as a Lie algebra not sufficient for Engel's theorem?

Approximating Heaviside function by twice differentiable, monotone sequence

Non-isomorphic groups with same number of homomorphisms

Does the Image of a Loop under Contraction contain a Disc?

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