Question

Is this a valid proof of $f:[a,b]\to\mathbb{R}$ continuous $\implies$ $f$ uniformly continuous?

score 168 · Answer 1 · 2015-07-14 20:08:10

168

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Is this a valid proof of $f:[a,b]\to\mathbb{R}$ continuous $\implies$ $f$ uniformly continuous?

Published on 14 Jul 2015 - 20:08

score 147 · Answer 2 · 2015-07-18 23:49:01

147

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topology of uniform convergence on compacts and strong operator topology

Published on 18 Jul 2015 - 23:49

score 7.9k · Answer 3 · 2015-07-21 06:11:43

7.9k

Views

Continuous and bounded imply uniform continuity?

Published on 21 Jul 2015 - 6:11

score 21.6k · Answer 4 · 2015-07-23 22:46:11

21.6k

Views

Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous

Published on 23 Jul 2015 - 22:46

score 18.2k · Answer 5 · 2015-07-25 00:58:48

18.2k

Views

Why is $f(x) = x^2$ uniformly continuous on [0,1] but not $\mathbb{R}$

Published on 25 Jul 2015 - 0:58

score 2.4k · Answer 6 · 2015-07-25 22:29:12

2.4k

Views

Why do we care if a function is uniformly continuous?

Published on 25 Jul 2015 - 22:29

score 82 · Answer 7 · 2015-07-26 11:09:55

82

Views

Exploit uniform continuity

Published on 26 Jul 2015 - 11:09

score 124 · Answer 8 · 2026-03-29 17:31:30

124

Views

"continuously differentiable $\subseteq$ Lipshitz continuous" with $f(x) = x^2$

Published on 29 Mar 2026 - 17:31

score 8.4k · Answer 9 · 2026-03-29 19:17:35

8.4k

Views

How to show square root of absolute of x, $\sqrt{|x|}$, is not Lipschitz continuous?

Published on 29 Mar 2026 - 19:17

score 1.2k · Answer 10 · 2026-03-26 07:55:13

1.2k

Views

What does Dini continuity mean?

Published on 26 Mar 2026 - 7:55

score 2.5k · Answer 11 · 2015-07-29 22:30:16

2.5k

Views

Uniform Continuity implies Continuity

Published on 29 Jul 2015 - 22:30

score 114 · Answer 12 · 2015-08-05 14:21:56

114

Views

Continuous function's property proof using slightly different epsilon/delta definition.

Published on 05 Aug 2015 - 14:21

score 170 · Answer 13 · 2015-08-05 16:32:44

170

Views

Prove uniformly continuity at $\infty$ to continuous function

Published on 05 Aug 2015 - 16:32

score 501 · Answer 14 · 2015-08-16 18:49:24

501

Views

Prove that function is not uniformly continuous

Published on 16 Aug 2015 - 18:49

score 117 · Answer 15 · 2015-08-17 08:05:16

117

Views

let $f$ be continuous on $[a,b]$. Prove that $f$ is integrable on $[a,b]$

Published on 17 Aug 2015 - 8:05

List Question

Is this a valid proof of $f:[a,b]\to\mathbb{R}$ continuous $\implies$ $f$ uniformly continuous?

topology of uniform convergence on compacts and strong operator topology

Continuous and bounded imply uniform continuity?

Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous

Why is $f(x) = x^2$ uniformly continuous on [0,1] but not $\mathbb{R}$

Why do we care if a function is uniformly continuous?

Exploit uniform continuity

"continuously differentiable $\subseteq$ Lipshitz continuous" with $f(x) = x^2$

How to show square root of absolute of x, $\sqrt{|x|}$, is not Lipschitz continuous?

What does Dini continuity mean?

Uniform Continuity implies Continuity

Continuous function's property proof using slightly different epsilon/delta definition.

Prove uniformly continuity at $\infty$ to continuous function

Prove that function is not uniformly continuous

let $f$ be continuous on $[a,b]$. Prove that $f$ is integrable on $[a,b]$

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