Question

Why is this sequence of equicontinuous functions uniformly bounded?

score 1.4k · Answer 1 · 2026-02-23 12:03:00

1.4k

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Why is this sequence of equicontinuous functions uniformly bounded?

Published on 23 Feb 2026 - 12:03

score 370 · Answer 2 · 2026-03-27 17:51:56

370

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When could no lipschitz still imply uniform continuity?

Published on 27 Mar 2026 - 17:51

score 109 · Answer 3 · 2016-11-02 21:08:21

109

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Proof that $f: \mathbb{R} \rightarrow \mathbb{R}$, $f(x)=x^k$ isn't uniformly continuous.

Published on 02 Nov 2016 - 21:08

score 219 · Answer 4 · 2016-11-04 05:01:30

219

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True or False: If $f \colon [a, \infty) \mathbb{R}$ is bounded and continuous, then $f$ is uniformly continuous on $[a, \infty)$

Published on 04 Nov 2016 - 5:01

score 303 · Answer 5 · 2016-11-06 20:01:00

303

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Using $\epsilon - \delta$ to show that $\sin\frac{1}{x}$ is not uniformly continuous

Published on 06 Nov 2016 - 20:01

score 5.4k · Answer 6 · 2016-11-07 19:01:10

5.4k

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If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous

Published on 07 Nov 2016 - 19:01

score 58 · Answer 7 · 2016-11-11 14:49:27

58

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Prove that $\sqrt[3]{a} - \sqrt[3]{b} < \sqrt[3]{a-b}$ by use of the MVT

Published on 11 Nov 2016 - 14:49

score 78 · Answer 8 · 2016-11-13 05:02:51

78

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Let $(g_n)$ be a sequence of functions on $[a,b]$. If $(g_n)$ converges pointwise and uniformly continuous on $[a,b]$

Published on 13 Nov 2016 - 5:02

score 1.5k · Answer 9 · 2026-03-29 16:00:46

1.5k

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Let $f:(0,1] \rightarrow \mathbb{R}$ be differentiable on $(0,1]$, with $|f'(x)| \leq 1$ let $a_n=f(1/n)$ Show that $(a_n)$converges.

Published on 29 Mar 2026 - 16:00

score 132 · Answer 10 · 2016-11-13 12:50:44

132

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Uniform Continuity: How can I show a continuous function $f: ]0,1] \rightarrow R $ is uniformly continuous if $\lim_{x \, \searrow \, 0}f(x) $ exists?

Published on 13 Nov 2016 - 12:50

score 976 · Answer 11 · 2016-11-14 09:56:15

976

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Prove uniform continuity of $e^{-x^2}$ on $\Bbb R$.

Published on 14 Nov 2016 - 9:56

score 272 · Answer 12 · 2016-11-14 18:29:04

272

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If $f_n \to f$ uniformly from $[a,b] \to \Bbb R$, every $f_n$ is continuous and each $f_n$ has a zero, then $f$ has a zero.

Published on 14 Nov 2016 - 18:29

score 86 · Answer 13 · 2016-11-15 01:57:45

86

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Let $(f_n)$ be a sequence of functions on $[a,b]$ such that each $f_n$ is continuous on $[a,b]$ and differentiable on $(a,b)$

Published on 15 Nov 2016 - 1:57

score 387 · Answer 14 · 2026-02-23 13:39:23

387

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question related to Lipschitz continuous function

Published on 23 Feb 2026 - 13:39

score 1.7k · Answer 15 · 2016-11-17 05:57:47

1.7k

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Example of a continuous function $f:\mathbb{R} \to [0,1]$ such that f is not uniformly continuous.

Published on 17 Nov 2016 - 5:57

List Question

Why is this sequence of equicontinuous functions uniformly bounded?

When could no lipschitz still imply uniform continuity?

Proof that $f: \mathbb{R} \rightarrow \mathbb{R}$, $f(x)=x^k$ isn't uniformly continuous.

True or False: If $f \colon [a, \infty) \mathbb{R}$ is bounded and continuous, then $f$ is uniformly continuous on $[a, \infty)$

Using $\epsilon - \delta$ to show that $\sin\frac{1}{x}$ is not uniformly continuous

If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous

Prove that $\sqrt[3]{a} - \sqrt[3]{b} < \sqrt[3]{a-b}$ by use of the MVT

Let $(g_n)$ be a sequence of functions on $[a,b]$. If $(g_n)$ converges pointwise and uniformly continuous on $[a,b]$

Let $f:(0,1] \rightarrow \mathbb{R}$ be differentiable on $(0,1]$, with $|f'(x)| \leq 1$ let $a_n=f(1/n)$ Show that $(a_n)$converges.

Uniform Continuity: How can I show a continuous function $f: ]0,1] \rightarrow R $ is uniformly continuous if $\lim_{x \, \searrow \, 0}f(x) $ exists?

Prove uniform continuity of $e^{-x^2}$ on $\Bbb R$.

If $f_n \to f$ uniformly from $[a,b] \to \Bbb R$, every $f_n$ is continuous and each $f_n$ has a zero, then $f$ has a zero.

Let $(f_n)$ be a sequence of functions on $[a,b]$ such that each $f_n$ is continuous on $[a,b]$ and differentiable on $(a,b)$

question related to Lipschitz continuous function

Example of a continuous function $f:\mathbb{R} \to [0,1]$ such that f is not uniformly continuous.

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