Question

Unique extension of a uniformly continuous function to the closure of its domain

score 858 · Answer 1 · 2022-07-15 00:33:24

858

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Unique extension of a uniformly continuous function to the closure of its domain

Published on 15 Jul 2022 - 0:33

score 59 · Answer 2 · 2022-07-18 08:13:19

59

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What does it mean by $\left|f(a)-f\left(b\right)\right| \leq \omega\left(d\left(x, x^{\prime}\right)\right) <+\infty$ if $f(a)= -\infty$?

Published on 18 Jul 2022 - 8:13

score 44 · Answer 3 · 2022-07-22 15:59:43

44

Views

Question regarding function series $\sum _{n=1}^{\infty }\sin\left(\frac{x}{n^2}\right)$ - continuity?

Published on 22 Jul 2022 - 15:59

score 716 · Answer 4 · 2026-02-27 09:31:24

716

Views

$f$ uniformly continuous, $f_n(x) = f(x + 1/n)$. Show $f_n$ uniformly converges to $f$. Why is uniform continuity needed?

Published on 27 Feb 2026 - 9:31

score 40 · Answer 5 · 2022-07-26 09:03:09

40

Views

Series of functions and uniform continuity

Published on 26 Jul 2022 - 9:03

score 76 · Answer 6 · 2022-08-08 10:22:15

76

Views

Proof of uniform continuity of a continuous function on an interval [a,b] without using compactness arguments

Published on 08 Aug 2022 - 10:22

score 86 · Answer 7 · 2026-02-23 06:38:05

86

Views

Does a homeomorphism on the unit disk, that is the identity on the boundary have bounded displacement?

Published on 23 Feb 2026 - 6:38

score 55 · Answer 8 · 2026-02-24 02:05:56

55

Views

Show that the sequence of functions converges uniformly.

Published on 24 Feb 2026 - 2:05

score 70 · Answer 9 · 2022-08-18 12:21:54

70

Views

Determining if a function is uniform continuous based on information of the limit of its derivative

Published on 18 Aug 2022 - 12:21

score 67 · Answer 10 · 2022-08-22 06:56:25

67

Views

Is saying "the function $f$ is uniformly continuous on I" the same as "the function is continous at each point of $I$"?

Published on 22 Aug 2022 - 6:56

score 63 · Answer 11 · 2022-08-22 14:07:25

63

Views

Is a function with uniformly continuous derivatives on a bounded regular domain also uniformly continuous?

Published on 22 Aug 2022 - 14:07

score 34 · Answer 12 · 2022-09-12 20:20:42

34

Views

Uniformly convergent subsequence of continuously differentiable functions with non-differentiable limit?

Published on 12 Sep 2022 - 20:20

score 123 · Answer 13 · 2026-04-01 05:43:48

123

Views

Example of a compact operator that is not uniformly continuous. [Solved]

Published on 01 Apr 2026 - 5:43

score 87 · Answer 14 · 2022-10-04 11:05:14

87

Views

Is $\log(x)$ uniformly continuous on $(\frac{1}{2},\infty)$?

Published on 04 Oct 2022 - 11:05

score 25 · Answer 15 · 2022-10-07 20:58:29

25

Views

Possible error in given definition of uniform continuity of a function on a metric space.

Published on 07 Oct 2022 - 20:58

List Question

Unique extension of a uniformly continuous function to the closure of its domain

What does it mean by $\left|f(a)-f\left(b\right)\right| \leq \omega\left(d\left(x, x^{\prime}\right)\right) <+\infty$ if $f(a)= -\infty$?

Question regarding function series $\sum _{n=1}^{\infty }\sin\left(\frac{x}{n^2}\right)$ - continuity?

$f$ uniformly continuous, $f_n(x) = f(x + 1/n)$. Show $f_n$ uniformly converges to $f$. Why is uniform continuity needed?

Series of functions and uniform continuity

Proof of uniform continuity of a continuous function on an interval [a,b] without using compactness arguments

Does a homeomorphism on the unit disk, that is the identity on the boundary have bounded displacement?

Show that the sequence of functions converges uniformly.

Determining if a function is uniform continuous based on information of the limit of its derivative

Is saying "the function $f$ is uniformly continuous on I" the same as "the function is continous at each point of $I$"?

Is a function with uniformly continuous derivatives on a bounded regular domain also uniformly continuous?

Uniformly convergent subsequence of continuously differentiable functions with non-differentiable limit?

Example of a compact operator that is not uniformly continuous. [Solved]

Is $\log(x)$ uniformly continuous on $(\frac{1}{2},\infty)$?

Possible error in given definition of uniform continuity of a function on a metric space.

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