List questions from uniform-continuity

Published on 01 Sep 2021 - 17:31

189

Views

(Uniform) convergence rate of fourier series under Holder-continuity

Published on 03 Sep 2021 - 0:42

78

Views

Prove (only with definition) that $f(x)=\frac{x^3+1}{x^2}, x>0$ is not uniformly continuous

Published on 06 Sep 2021 - 11:02

123

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If a sequence $f_n$ converges uniformly to $f$, then the Riemann integral $\lim_{n\to\infty}\int f_n=\int f$ - is my proof correct?

Published on 11 Sep 2021 - 13:10

68

Views

Uniform continuity on a finite interval

Published on 15 Sep 2021 - 19:00

67

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Is $T$ uniformly continous?

Published on 15 Sep 2021 - 22:17

1.3k

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Does a continuous function map Cauchy sequences to Cauchy sequences?

Published on 16 Sep 2021 - 10:58

112

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

Published on 16 Sep 2021 - 11:59

536

Views

Example of a continuous but not uniformly continuous function $f:Y\to Y$ on a complete convex bounded subset $Y$ of a metric space $X$.

Published on 20 Sep 2021 - 10:37

73

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Does there exist an example of such a pathological continuous function?

Published on 21 Sep 2021 - 12:18

79

Views

On proving uniform continuity

Published on 26 Sep 2021 - 18:26

151

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$\sin\left(\frac 1x\right)$ is not uniformly continuous in $(0,1)$ - is my proof correct?

Published on 27 Sep 2021 - 20:17

642

Views

When does Cauchy continuity imply uniform continuity?

Published on 29 Sep 2021 - 9:37

73

Views

Continuous extension in the proof of Arzela - Ascoli theorem

Published on 23 Feb 2026 - 21:37

106

Views

On the behavior at infinity of an integrable function

Published on 05 Oct 2021 - 17:53

List Question

Question regarding sequential criteria for continuity and uniform continuity

(Uniform) convergence rate of fourier series under Holder-continuity

Prove (only with definition) that $f(x)=\frac{x^3+1}{x^2}, x>0$ is not uniformly continuous

If a sequence $f_n$ converges uniformly to $f$, then the Riemann integral $\lim_{n\to\infty}\int f_n=\int f$ - is my proof correct?

Uniform continuity on a finite interval

Is $T$ uniformly continous?

Does a continuous function map Cauchy sequences to Cauchy sequences?

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

Example of a continuous but not uniformly continuous function $f:Y\to Y$ on a complete convex bounded subset $Y$ of a metric space $X$.

Does there exist an example of such a pathological continuous function?

On proving uniform continuity

$\sin\left(\frac 1x\right)$ is not uniformly continuous in $(0,1)$ - is my proof correct?

When does Cauchy continuity imply uniform continuity?

Continuous extension in the proof of Arzela - Ascoli theorem

On the behavior at infinity of an integrable function

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