Question

$f:\mathbb{R}\rightarrow [0,\infty)$ is continuous and $f^2$ is uniformly continuous then f is uniformly continuous

score 54 · Answer 1 · 2022-10-08 15:20:59

54

Views

$f:\mathbb{R}\rightarrow [0,\infty)$ is continuous and $f^2$ is uniformly continuous then f is uniformly continuous

Published on 08 Oct 2022 - 15:20

score 518 · Answer 2 · 2022-10-08 18:07:07

518

Views

$f:(a,b)\to \mathbb{R}$ is uniformly continuous $\implies f$ is bounded.

Published on 08 Oct 2022 - 18:07

score 216 · Answer 3 · 2022-10-09 14:13:15

216

Views

Prove that $x\sin(x)$ is continuous at $x = 0$

Published on 09 Oct 2022 - 14:13

score 265 · Answer 4 · 2022-10-10 08:43:03

265

Views

Example of a uniformly continuous function on R but with derivative not uniformly continuous.

Published on 10 Oct 2022 - 8:43

score 713 · Answer 5 · 2022-10-11 05:33:52

713

Views

Proof that if $f(x)$ is continuous on $[a,b]$ it is uniformly continuous on $[a,b]$

Published on 11 Oct 2022 - 5:33

score 101 · Answer 6 · 2022-10-11 17:31:04

101

Views

Example of a function from $\Bbb Z$ to $\Bbb Z$ continuous but not uniformly continuous for the $p$-adic metric.

Published on 11 Oct 2022 - 17:31

score 62 · Answer 7 · 2022-10-11 22:11:15

62

Views

Directly showing uniform continuity from continuity of $f(x)$ on $[a,b]$

Published on 11 Oct 2022 - 22:11

score 31 · Answer 8 · 2022-10-12 13:03:59

31

Views

Does the extension of uniformly continuous functions uniformly continuous?

Published on 12 Oct 2022 - 13:03

score 85 · Answer 9 · 2022-10-18 19:01:29

85

Views

Undergraduate Real Analysis problem books that do not require Topology

Published on 18 Oct 2022 - 19:01

score 72 · Answer 10 · 2022-10-25 05:44:54

72

Views

What is an example of a function that is uniformly continuous but not continuous on an interval $[a,b]$?

Published on 25 Oct 2022 - 5:44

score 59 · Answer 11 · 2022-11-07 12:01:32

59

Views

Existence of continuous functions with finitely many prescribed values

Published on 07 Nov 2022 - 12:01

score 137 · Answer 12 · 2022-11-09 18:44:12

137

Views

Riemann Integral and Limits in Exercise 5 Section 1B of Measure, Integration & Real Analysis by Sheldon Axler

Published on 09 Nov 2022 - 18:44

score 67 · Answer 13 · 2026-02-24 03:42:50

67

Views

Uniform continuous, equicontinuity, and Banach-Steinhaus

Published on 24 Feb 2026 - 3:42

score 35 · Answer 14 · 2022-11-17 19:38:06

35

Views

proof: show that f'(x) is uniformly continuous on I.

Published on 17 Nov 2022 - 19:38

score 69 · Answer 15 · 2026-03-28 04:00:49

69

Views

Uniform continuity and seminorms

Published on 28 Mar 2026 - 4:00

List Question

$f:\mathbb{R}\rightarrow [0,\infty)$ is continuous and $f^2$ is uniformly continuous then f is uniformly continuous

$f:(a,b)\to \mathbb{R}$ is uniformly continuous $\implies f$ is bounded.

Prove that $x\sin(x)$ is continuous at $x = 0$

Example of a uniformly continuous function on R but with derivative not uniformly continuous.

Proof that if $f(x)$ is continuous on $[a,b]$ it is uniformly continuous on $[a,b]$

Example of a function from $\Bbb Z$ to $\Bbb Z$ continuous but not uniformly continuous for the $p$-adic metric.

Directly showing uniform continuity from continuity of $f(x)$ on $[a,b]$

Does the extension of uniformly continuous functions uniformly continuous?

Undergraduate Real Analysis problem books that do not require Topology

What is an example of a function that is uniformly continuous but not continuous on an interval $[a,b]$?

Existence of continuous functions with finitely many prescribed values

Riemann Integral and Limits in Exercise 5 Section 1B of Measure, Integration & Real Analysis by Sheldon Axler

Uniform continuous, equicontinuity, and Banach-Steinhaus

proof: show that f'(x) is uniformly continuous on I.

Uniform continuity and seminorms

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