Question

Is the uniform limit of uniformly continuous functions, uniformly continuous itself?

score 6.5k · Answer 1 · 2026-02-25 17:55:19

6.5k

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Is the uniform limit of uniformly continuous functions, uniformly continuous itself?

Published on 25 Feb 2026 - 17:55

score 27.5k · Answer 2 · 2010-10-27 16:25:24

27.5k

Views

Is the distance function in a metric space (uniformly) continuous?

Published on 27 Oct 2010 - 16:25

score 7.4k · Answer 3 · 2011-02-27 19:38:31

7.4k

Views

Uniform continuity on (0,1) implies boundedness

Published on 27 Feb 2011 - 19:38

score 30.7k · Answer 4 · 2011-10-24 19:17:38

30.7k

Views

How does the existence of a limit imply that a function is uniformly continuous

Published on 24 Oct 2011 - 19:17

score 73.4k · Answer 5 · 2026-02-24 06:47:27

73.4k

Views

Continuous mapping on a compact metric space is uniformly continuous

Published on 24 Feb 2026 - 6:47

score 9.3k · Answer 6 · 2012-03-10 21:23:48

9.3k

Views

Why if $f'$ is unbounded, then $f$ isn't uniformly continuous?

Published on 10 Mar 2012 - 21:23

score 16.2k · Answer 7 · 2012-04-01 16:35:01

16.2k

Views

If $f'$ is bounded, then $f$ is uniformly continuous

Published on 01 Apr 2012 - 16:35

score 5.7k · Answer 8 · 2012-04-22 12:07:44

5.7k

Views

Showing $f(x)=x^4$ is not uniformly continuous

Published on 22 Apr 2012 - 12:07

score 714 · Answer 9 · 2012-05-04 06:12:02

714

Views

Cauchy sequence under uniformly continuous function

Published on 04 May 2012 - 6:12

score 1.3k · Answer 10 · 2012-05-05 16:05:19

1.3k

Views

Extending functions from $(a,b)$ to $[a,b]$.

Published on 05 May 2012 - 16:05

score 8.2k · Answer 11 · 2012-08-12 07:38:13

8.2k

Views

How to prove $x^{n}$ is not uniformly continuous

Published on 12 Aug 2012 - 7:38

score 10.2k · Answer 12 · 2012-10-11 14:43:50

10.2k

Views

Relation between uniform continuity and uniform convergence

Published on 11 Oct 2012 - 14:43

score 42.5k · Answer 13 · 2012-10-22 21:26:23

42.5k

Views

Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.

Published on 22 Oct 2012 - 21:26

score 24.4k · Answer 14 · 2012-10-25 10:30:59

24.4k

Views

Is a bounded and continuous function uniformly continuous?

Published on 25 Oct 2012 - 10:30

score 18k · Answer 15 · 2026-03-29 15:14:55

18k

Views

Extension of a Uniformly Continuous Function between Metric Spaces

Published on 29 Mar 2026 - 15:14

List Question

Is the uniform limit of uniformly continuous functions, uniformly continuous itself?

Is the distance function in a metric space (uniformly) continuous?

Uniform continuity on (0,1) implies boundedness

How does the existence of a limit imply that a function is uniformly continuous

Continuous mapping on a compact metric space is uniformly continuous

Why if $f'$ is unbounded, then $f$ isn't uniformly continuous?

If $f'$ is bounded, then $f$ is uniformly continuous

Showing $f(x)=x^4$ is not uniformly continuous

Cauchy sequence under uniformly continuous function

Extending functions from $(a,b)$ to $[a,b]$.

How to prove $x^{n}$ is not uniformly continuous

Relation between uniform continuity and uniform convergence

Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.

Is a bounded and continuous function uniformly continuous?

Extension of a Uniformly Continuous Function between Metric Spaces

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