List questions from uniform-continuity

Published on 27 Jan 2016 - 19:15

73

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$f(x,y)=\frac{(x,y)}{\|(x,y)\|^2}$ - Show that $f$ is not uniformly continuous

Published on 30 Jan 2016 - 23:05

68

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Show that the function $h : A \to F \times G$ defined by $h(x) = (f(x), g(x))$ is uniformly continuous.

Published on 01 Feb 2016 - 22:38

591

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Show that $\lim_{x \to x_0} f(x)$ exist

Published on 02 Feb 2016 - 14:10

4.4k

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Showing that a function is uniformly continuous but not Lipschitz

Published on 30 Mar 2026 - 5:25

1.7k

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Is $C_0(\mathbb{R})$ a Banach space?

Published on 03 Feb 2016 - 15:28

75

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Equicontinuous homotopies of families of uniformly equicontinuous functions

Published on 27 Mar 2026 - 7:16

153

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Showing uniform continuity for two intervals

Published on 04 Feb 2016 - 17:21

683

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Is $\frac{1}{\sin x}-\frac{1}{x}$ uniformly continuous on $(0,1)$?

Published on 04 Feb 2016 - 17:27

52

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Completeness of a certain normed space

Published on 04 Feb 2016 - 17:43

608

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Show $\cos(x^2)/(1+ x^2)$ is uniformly continuous on $\Bbb R$.

Published on 04 Feb 2016 - 19:12

37

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Uniformly continuous of a function

Published on 04 Feb 2016 - 20:50

1.6k

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is $x\sin(\frac{1}{x^2})$ uniformly continuous on $(0,1]$?

Published on 04 Feb 2016 - 22:07

166

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Show that $f$ is uniformly continuous - Compactness

Published on 06 Feb 2016 - 19:07

135

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Show that $f$ is uniformly continuous - $\lim_{\|x\| \to \infty}f(x) = c$

Published on 06 Feb 2016 - 23:36

List Question

Supremum and infimum of continuous functions on $[a,b]$

$f(x,y)=\frac{(x,y)}{\|(x,y)\|^2}$ - Show that $f$ is not uniformly continuous

Show that the function $h : A \to F \times G$ defined by $h(x) = (f(x), g(x))$ is uniformly continuous.

Show that $\lim_{x \to x_0} f(x)$ exist

Showing that a function is uniformly continuous but not Lipschitz

Is $C_0(\mathbb{R})$ a Banach space?

Equicontinuous homotopies of families of uniformly equicontinuous functions

Showing uniform continuity for two intervals

Is $\frac{1}{\sin x}-\frac{1}{x}$ uniformly continuous on $(0,1)$?

Completeness of a certain normed space

Show $\cos(x^2)/(1+ x^2)$ is uniformly continuous on $\Bbb R$.

Uniformly continuous of a function

is $x\sin(\frac{1}{x^2})$ uniformly continuous on $(0,1]$?

Show that $f$ is uniformly continuous - Compactness

Show that $f$ is uniformly continuous - $\lim_{\|x\| \to \infty}f(x) = c$

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