Question

If there exists a uniformly continuous homeomorphism from a metric space $X$ to a complete metric space $Y$ then is $X$ complete?

score 283 · Answer 1 · 2026-03-26 22:18:19

283

Views

If there exists a uniformly continuous homeomorphism from a metric space $X$ to a complete metric space $Y$ then is $X$ complete?

Published on 26 Mar 2026 - 22:18

score 213 · Answer 2 · 2026-03-27 16:28:10

213

Views

If $V,W$ are Banach spaces, $\Omega\subseteq V$ is open, $f:\Omega\to W$ is differentiable and ${\rm D}f$ is bounded, then $f$ is Lipschitz continuous

Published on 27 Mar 2026 - 16:28

score 463 · Answer 3 · 2016-09-08 12:19:47

463

Views

Uniform continuity of $\sin(x\sin x )$ for all $x\in (0,\infty)$

Published on 08 Sep 2016 - 12:19

score 101 · Answer 4 · 2016-09-14 12:13:38

101

Views

Is $\sqrt{|x|}$ uniformly continuous from $\mathbb{R}\to\mathbb{R}$?

Published on 14 Sep 2016 - 12:13

score 142 · Answer 5 · 2016-09-14 12:53:30

142

Views

Bounds for uniformly continuous function

Published on 14 Sep 2016 - 12:53

score 1.6k · Answer 6 · 2026-03-27 00:02:30

1.6k

Views

Why do uniformly continuous functions form a Banach space (with the sup norm)?

Published on 27 Mar 2026 - 0:02

score 273 · Answer 7 · 2016-09-18 13:37:59

273

Views

Cauchy sequences and their importance

Published on 18 Sep 2016 - 13:37

score 498 · Answer 8 · 2016-09-18 20:07:39

498

Views

Limit of cauchy sequence of uniformly continuous functions is uniformly continuous

Published on 18 Sep 2016 - 20:07

score 2.5k · Answer 9 · 2026-03-28 10:54:44

2.5k

Views

Is the matrix square root uniformly continuous?

Published on 28 Mar 2026 - 10:54

score 74 · Answer 10 · 2016-09-25 04:01:49

74

Views

Uniform continuity and the sine function.

Published on 25 Sep 2016 - 4:01

score 1.9k · Answer 11 · 2016-09-26 16:31:46

1.9k

Views

Show that the cumulative distribution function is uniformly continuous.

Published on 26 Sep 2016 - 16:31

score 431 · Answer 12 · 2016-09-29 17:46:01

431

Views

Is every uniformly continuous mapping also continuous?

Published on 29 Sep 2016 - 17:46

score 52 · Answer 13 · 2016-10-02 17:16:51

52

Views

How to check whether $f$ is uniformly continuous

Published on 02 Oct 2016 - 17:16

score 284 · Answer 14 · 2016-10-05 09:30:12

284

Views

Unbounded domain, existence of continuous fcn that is not uniformly continuous.

Published on 05 Oct 2016 - 9:30

score 74 · Answer 15 · 2016-10-09 17:01:13

74

Views

What subsets of $\mathbb R$ can we speak of uniform continuity?

Published on 09 Oct 2016 - 17:01

List Question

If there exists a uniformly continuous homeomorphism from a metric space $X$ to a complete metric space $Y$ then is $X$ complete?

If $V,W$ are Banach spaces, $\Omega\subseteq V$ is open, $f:\Omega\to W$ is differentiable and ${\rm D}f$ is bounded, then $f$ is Lipschitz continuous

Uniform continuity of $\sin(x\sin x )$ for all $x\in (0,\infty)$

Is $\sqrt{|x|}$ uniformly continuous from $\mathbb{R}\to\mathbb{R}$?

Bounds for uniformly continuous function

Why do uniformly continuous functions form a Banach space (with the sup norm)?

Cauchy sequences and their importance

Limit of cauchy sequence of uniformly continuous functions is uniformly continuous

Is the matrix square root uniformly continuous?

Uniform continuity and the sine function.

Show that the cumulative distribution function is uniformly continuous.

Is every uniformly continuous mapping also continuous?

How to check whether $f$ is uniformly continuous

Unbounded domain, existence of continuous fcn that is not uniformly continuous.

What subsets of $\mathbb R$ can we speak of uniform continuity?

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