Question

Let $\mathbb{Z}$ be the integers with the discrete topology. Let $f: \mathbb{Z} \to \mathbb{R}$. Give conditions to have $f$ continuous.

score 81 · Answer 1 · 2018-12-10 16:39:01

81

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Let $\mathbb{Z}$ be the integers with the discrete topology. Let $f: \mathbb{Z} \to \mathbb{R}$. Give conditions to have $f$ continuous.

Published on 10 Dec 2018 - 16:39

score 3.7k · Answer 2 · 2026-03-25 19:04:13

3.7k

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Prove inverse of strictly monotone increasing function is continuous over the range of original function

Published on 25 Mar 2026 - 19:04

score 604 · Answer 3 · 2026-03-26 01:01:13

604

Views

Space filling curve

Published on 26 Mar 2026 - 1:01

score 1k · Answer 4 · 2026-03-27 14:52:22

1k

Views

How to solve $\dot{x} = \frac{f(x)}{\|f(x)\|}$?

Published on 27 Mar 2026 - 14:52

score 707 · Answer 5 · 2026-03-25 06:21:41

707

Views

Show that given a proper map, for each closed set F its image f(F) is closed

Published on 25 Mar 2026 - 6:21

score 39 · Answer 6 · 2026-03-25 03:24:14

39

Views

Show that the functional is continuous

Published on 25 Mar 2026 - 3:24

score 537 · Answer 7 · 2018-12-11 18:32:19

537

Views

How to show the function $f(x) = x^2 \sin(1/x)$ has integrable derivative?

Published on 11 Dec 2018 - 18:32

score 55 · Answer 8 · 2026-03-29 13:40:46

55

Views

Show that the functional $F$ on $L_p(-1,1)$ given by $ F(f) = \int_{-1}^0 f(t)dt - \int_{0}^1 f(t)dt $ is continuous.

Published on 29 Mar 2026 - 13:40

score 209 · Answer 9 · 2018-12-11 22:15:03

209

Views

Is this function continuous everywhere or at 1 point only?

Published on 11 Dec 2018 - 22:15

score 345 · Answer 10 · 2026-03-25 20:41:18

345

Views

Why is an elementary Ito integral necessarily continuous?

Published on 25 Mar 2026 - 20:41

score 36 · Answer 11 · 2018-12-12 04:58:50

I understand I can show the function $e ^ x$ is continuous at point $0$, by means of the definition epsilon delta. But which epsilon I should take?

score 57 · Answer 12 · 2018-12-12 06:51:01

57

Views

Finding an example of a function $f(x)$ that is differentiable on $(a,b)$ but $f'(x)$ is not continuous on $(a,b)$.

Published on 12 Dec 2018 - 6:51

score 76 · Answer 13 · 2026-03-28 23:57:38

76

Views

Is continuous increasing function in $H^1([0,1])$

Published on 28 Mar 2026 - 23:57

score 68 · Answer 14 · 2018-12-13 06:42:47

68

Views

Continuous map example

Published on 13 Dec 2018 - 6:42

score 46 · Answer 15 · 2018-12-13 13:40:13

46

Views

How about $f(x)g(x)$?

Published on 13 Dec 2018 - 13:40

List Question

Let $\mathbb{Z}$ be the integers with the discrete topology. Let $f: \mathbb{Z} \to \mathbb{R}$. Give conditions to have $f$ continuous.

Prove inverse of strictly monotone increasing function is continuous over the range of original function

Space filling curve

How to solve $\dot{x} = \frac{f(x)}{\|f(x)\|}$?

Show that given a proper map, for each closed set F its image f(F) is closed

Show that the functional is continuous

How to show the function $f(x) = x^2 \sin(1/x)$ has integrable derivative?

Show that the functional $F$ on $L_p(-1,1)$ given by $ F(f) = \int_{-1}^0 f(t)dt - \int_{0}^1 f(t)dt $ is continuous.

Is this function continuous everywhere or at 1 point only?

Why is an elementary Ito integral necessarily continuous?

I understand I can show the function $e ^ x$ is continuous at point $0$, by means of the definition epsilon delta. But which epsilon I should take?

Finding an example of a function $f(x)$ that is differentiable on $(a,b)$ but $f'(x)$ is not continuous on $(a,b)$.

Is continuous increasing function in $H^1([0,1])$

Continuous map example

How about $f(x)g(x)$?

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