List questions from uniform-continuity

Published on 30 Nov 2015 - 18:03

2.1k

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Is a continuous function locally uniformly continuous?

Published on 01 Dec 2015 - 12:48

182

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Unexpectedly uniformly continuous functions

Published on 30 Mar 2026 - 3:50

148

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Uniform Continuity & Cauchy Sequences

Published on 02 Dec 2015 - 3:14

454

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Showing continuity of a multivariable function continuous in each variable, with $x\mapsto f(x,y)$ for fixed $y$ being equicontinuous

Published on 02 Dec 2015 - 8:00

214

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Check uniform equicontinuity of a function family

Published on 04 Dec 2015 - 18:22

2k

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Continuous function that is uniformly continuous on a dense subset

Published on 05 Dec 2015 - 22:43

409

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Show that if $f$ is a uniformly continuous function on $\mathbb{R}$ and $f\in L^1(\mathbb{R})$, then $f$ is bounded and $\lim_{|x|\to\infty}f(x)=0$.

Published on 06 Dec 2015 - 8:35

3.2k

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For uniformly continuous $f:X\to Y$, where $X$ is a totally bounded metric space, prove that $f(X)$ is totally bounded

Published on 07 Dec 2015 - 13:28

757

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Analysis: Prove that this function is not uniformly continuous on the interval $(0,1)$

Published on 08 Dec 2015 - 17:13

816

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continuity of Power Series on Boundary

Published on 08 Dec 2015 - 22:23

1.2k

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Show $f(x)=\sqrt{x}$ is uniformly continuous on $[0,\infty)$

Published on 10 Dec 2015 - 1:41

524

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If $f$ is uniformly continuous on $(a,b)$, is $f$ uniformly continuous on $[a,b]$?

Published on 10 Dec 2015 - 4:46

61

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Uniformly continuity of the function.

Published on 10 Dec 2015 - 19:31

100

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Obscure proof for $f\in \mathcal C_0(\mathbb R)\implies U_f\in u_f$ continuous.

Published on 12 Dec 2015 - 22:36

List Question

Is $\cos^3{x}$ uniformly continuous?

Is a continuous function locally uniformly continuous?

Unexpectedly uniformly continuous functions

Uniform Continuity & Cauchy Sequences

Showing continuity of a multivariable function continuous in each variable, with $x\mapsto f(x,y)$ for fixed $y$ being equicontinuous

Check uniform equicontinuity of a function family

Continuous function that is uniformly continuous on a dense subset

Show that if $f$ is a uniformly continuous function on $\mathbb{R}$ and $f\in L^1(\mathbb{R})$, then $f$ is bounded and $\lim_{|x|\to\infty}f(x)=0$.

For uniformly continuous $f:X\to Y$, where $X$ is a totally bounded metric space, prove that $f(X)$ is totally bounded

Analysis: Prove that this function is not uniformly continuous on the interval $(0,1)$

continuity of Power Series on Boundary

Show $f(x)=\sqrt{x}$ is uniformly continuous on $[0,\infty)$

If $f$ is uniformly continuous on $(a,b)$, is $f$ uniformly continuous on $[a,b]$?

Uniformly continuity of the function.

Obscure proof for $f\in \mathcal C_0(\mathbb R)\implies U_f\in u_f$ continuous.

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