Question

uniformly continuous function $f$ such that $\sum 1/f(n)$ is convergent?

score 1.4k · Answer 1 · 2018-12-11 21:23:28

1.4k

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uniformly continuous function $f$ such that $\sum 1/f(n)$ is convergent?

Published on 11 Dec 2018 - 21:23

score 2.7k · Answer 2 · 2018-12-12 22:41:18

2.7k

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Proving that a differentiable function f, with f' bounded, is uniformly continuous

Published on 12 Dec 2018 - 22:41

score 100 · Answer 3 · 2018-12-14 17:03:14

100

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Is $f:(-1,1)\to R$ defined as $f(x)= \frac{x}{1-\lvert x \rvert}$ and $f^{-1}(x)$ uniformly continuos?

Published on 14 Dec 2018 - 17:03

score 77 · Answer 4 · 2018-12-14 17:07:23

77

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How to prove $x^{1/n} $ is uniformly continuos in $[0, a]$ where $a$ is a positive real.

Published on 14 Dec 2018 - 17:07

score 98 · Answer 5 · 2026-03-26 11:18:23

98

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Prove tht $f(x) = x^{2}$ is uniformly continuous on $\bigcup_{n = 1}^{\infty} [n, n + 1/n^{3}]$.

Published on 26 Mar 2026 - 11:18

score 198 · Answer 6 · 2018-12-17 12:56:10

198

Views

Nearest point property and uniformly continuous image

Published on 17 Dec 2018 - 12:56

score 79 · Answer 7 · 2026-03-26 03:00:27

79

Views

Identical Cauchy sequences and continuity.

Published on 26 Mar 2026 - 3:00

score 39 · Answer 8 · 2018-12-18 14:00:46

39

Views

Determine if the function is uniformly continuous

Published on 18 Dec 2018 - 14:00

score 64 · Answer 9 · 2018-12-18 17:04:38

64

Views

Uniform Continuity of sum of a series of functions

Published on 18 Dec 2018 - 17:04

score 266 · Answer 10 · 2018-12-18 19:15:55

266

Views

If a function is uniformly continuous restricted to each line, is it globally uniformly continuous?

Published on 18 Dec 2018 - 19:15

score 536 · Answer 11 · 2018-12-19 23:52:50

536

Views

If $f:[0,1] \rightarrow \mathbb{R}$ is continuous then it is uniformly continuous

Published on 19 Dec 2018 - 23:52

score 39 · Answer 12 · 2018-12-20 11:19:18

39

Views

On uniform convergence of function

Published on 20 Dec 2018 - 11:19

score 341 · Answer 13 · 2026-02-23 01:05:19

341

Views

Do the metrics $d$ and $\frac{d}{1+d}$ induce the same uniformity?

Published on 23 Feb 2026 - 1:05

score 168 · Answer 14 · 2018-12-23 11:49:44

168

Views

Proving uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ on $(1,2)$ directly from the definition.

Published on 23 Dec 2018 - 11:49

score 145 · Answer 15 · 2026-03-25 19:25:19

145

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If $f$ is $C^{1}$ and $\sup_{x \in \mathbb{R}}|f'(x)| = \infty$ , prove that $f$ cannot be uniformly continuous

Published on 25 Mar 2026 - 19:25

List Question

uniformly continuous function $f$ such that $\sum 1/f(n)$ is convergent?

Proving that a differentiable function f, with f' bounded, is uniformly continuous

Is $f:(-1,1)\to R$ defined as $f(x)= \frac{x}{1-\lvert x \rvert}$ and $f^{-1}(x)$ uniformly continuos?

How to prove $x^{1/n} $ is uniformly continuos in $[0, a]$ where $a$ is a positive real.

Prove tht $f(x) = x^{2}$ is uniformly continuous on $\bigcup_{n = 1}^{\infty} [n, n + 1/n^{3}]$.

Nearest point property and uniformly continuous image

Identical Cauchy sequences and continuity.

Determine if the function is uniformly continuous

Uniform Continuity of sum of a series of functions

If a function is uniformly continuous restricted to each line, is it globally uniformly continuous?

If $f:[0,1] \rightarrow \mathbb{R}$ is continuous then it is uniformly continuous

On uniform convergence of function

Do the metrics $d$ and $\frac{d}{1+d}$ induce the same uniformity?

Proving uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ on $(1,2)$ directly from the definition.

If $f$ is $C^{1}$ and $\sup_{x \in \mathbb{R}}|f'(x)| = \infty$ , prove that $f$ cannot be uniformly continuous

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