Question

$\lim_n{f(\frac{x}{n})}=0$, for all $x\in (0,1)$ implies $lim_{x\to0}f(x)=0$ (edit, $f$ is not continuous)

score 60 · Answer 1 · 2019-01-27 01:08:01

60

Views

$\lim_n{f(\frac{x}{n})}=0$, for all $x\in (0,1)$ implies $lim_{x\to0}f(x)=0$ (edit, $f$ is not continuous)

Published on 27 Jan 2019 - 1:08

score 1.1k · Answer 2 · 2019-01-27 11:14:43

1.1k

Views

Intermediate Value Theorem in $ \mathbb{R}^2$ and $ \mathbb{R}^3$

Published on 27 Jan 2019 - 11:14

score 28 · Answer 3 · 2026-03-27 06:15:07

28

Views

Any continuous mapping on compact set is uniformly continous

Published on 27 Mar 2026 - 6:15

score 37 · Answer 4 · 2019-01-27 18:53:55

37

Views

If $f(a_{n_k}) \to a$ as $k \to \infty$, then there is some $x \in \mathbb{R}$ such that $f(x) = a$ and $a_{n_k} \to x$.

Published on 27 Jan 2019 - 18:53

score 38 · Answer 5 · 2019-01-27 20:20:56

38

Views

Continuity on Interval

Published on 27 Jan 2019 - 20:20

score 43 · Answer 6 · 2026-03-28 20:53:44

43

Views

Can we apply IVT to solve this?

Published on 28 Mar 2026 - 20:53

score 175 · Answer 7 · 2019-01-28 03:14:32

175

Views

Prove that there is a first time the function is zero

Published on 28 Jan 2019 - 3:14

score 121 · Answer 8 · 2019-01-28 04:52:10

121

Views

Continuous function (Topology)

Published on 28 Jan 2019 - 4:52

score 233 · Answer 9 · 2026-03-25 23:36:26

233

Views

Every continuous open mapping from $\mathbb{R}$ into $\mathbb{R}$ is monotonic

Published on 25 Mar 2026 - 23:36

score 46 · Answer 10 · 2026-03-26 16:56:55

46

Views

If $\beta$ is a continuous function with $\beta f'=0$ for all $f\in C_c^\infty$, are we able to conclude $\beta=0$?

Published on 26 Mar 2026 - 16:56

score 285 · Answer 11 · 2026-04-04 12:31:52

285

Views

Are linear transformations between infinite dimensional vector spaces always differentiable?

Published on 04 Apr 2026 - 12:31

score 2.8k · Answer 12 · 2019-01-29 20:09:07

2.8k

Views

But what is a continuous function?

Published on 29 Jan 2019 - 20:09

score 68 · Answer 13 · 2019-01-30 15:14:49

68

Views

Prove discontinuity of $U(f)= f^3$

Published on 30 Jan 2019 - 15:14

score 24 · Answer 14 · 2026-03-30 15:35:07

24

Views

A characteristic continuous mapping

Published on 30 Mar 2026 - 15:35

score 128 · Answer 15 · 2019-01-30 22:33:20

128

Views

If $f(x)$ is continuous, then $f(x+t)$ is continuous.

Published on 30 Jan 2019 - 22:33

List Question

$\lim_n{f(\frac{x}{n})}=0$, for all $x\in (0,1)$ implies $lim_{x\to0}f(x)=0$ (edit, $f$ is not continuous)

Intermediate Value Theorem in $ \mathbb{R}^2$ and $ \mathbb{R}^3$

Any continuous mapping on compact set is uniformly continous

If $f(a_{n_k}) \to a$ as $k \to \infty$, then there is some $x \in \mathbb{R}$ such that $f(x) = a$ and $a_{n_k} \to x$.

Continuity on Interval

Can we apply IVT to solve this?

Prove that there is a first time the function is zero

Continuous function (Topology)

Every continuous open mapping from $\mathbb{R}$ into $\mathbb{R}$ is monotonic

If $\beta$ is a continuous function with $\beta f'=0$ for all $f\in C_c^\infty$, are we able to conclude $\beta=0$?

Are linear transformations between infinite dimensional vector spaces always differentiable?

But what is a continuous function?

Prove discontinuity of $U(f)= f^3$

A characteristic continuous mapping

If $f(x)$ is continuous, then $f(x+t)$ is continuous.

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