Question

If I am asked to prove whether or not a function is uniformly continuous, how can I determine whether it is or is not before constructing the proof?

score 34 · Answer 1 · 2023-04-05 14:43:03

34

Views

If I am asked to prove whether or not a function is uniformly continuous, how can I determine whether it is or is not before constructing the proof?

Published on 05 Apr 2023 - 14:43

score 301 · Answer 2 · 2023-04-18 03:04:30

301

Views

Prove that if $X$ is compact, then every continuous function $f: X \to Y$ is uniformly continuous

Published on 18 Apr 2023 - 3:04

score 76 · Answer 3 · 2026-03-26 06:25:35

76

Views

Is the Pontryagin map uniformly continuous?

Published on 26 Mar 2026 - 6:25

score 95 · Answer 4 · 2023-04-21 10:12:48

95

Views

Showing $\displaystyle \lim_{(t_1,t_2) \to (t,t), t_1 < t_2} \frac{\gamma(t_2)-\gamma(t_1)}{t_2-t_1}=\gamma'(t)$ ( using uniform continuity )

Published on 21 Apr 2023 - 10:12

score 61 · Answer 5 · 2023-04-24 08:10:00

61

Views

How to show function is uniformly continuous over metric spaces.

Published on 24 Apr 2023 - 8:10

score 85 · Answer 6 · 2023-04-25 16:19:34

85

Views

(Uniform) continuous function $f : [0,\infty) \rightarrow \mathbb R$ is Lebesgue integrable, then $\lim_{x\rightarrow \infty} f(x) =0$?

Published on 25 Apr 2023 - 16:19

score 81 · Answer 7 · 2023-04-25 19:38:07

81

Views

Is there an analogue of uniform continuity for multivariable functions? And, is addition and multiplication uniformly continuous?

Published on 25 Apr 2023 - 19:38

score 62 · Answer 8 · 2023-04-25 22:42:14

62

Views

Let $f$ be continuous on an open interval $(a,b)$, and let its limits at $a$ and $b$ exist. Show that $f$ is uniformly continuous on the interval.

Published on 25 Apr 2023 - 22:42

score 121 · Answer 9 · 2026-03-25 17:25:06

121

Views

What is the space $BUC^s$?

Published on 25 Mar 2026 - 17:25

score 105 · Answer 10 · 2023-04-30 02:28:19

105

Views

Uniform continuity (in terms of Big-O notation)

Published on 30 Apr 2023 - 2:28

score 26 · Answer 11 · 2023-05-09 14:21:27

26

Views

$f: (X,d) \rightarrow (X',d')$ uniformly continuous and $A,B \subseteq E: \ d(A,B) = 0 \Rightarrow d'(f(A),f(B))=0$

Published on 09 May 2023 - 14:21

score 82 · Answer 12 · 2023-05-09 14:53:51

82

Views

If $f$ is continuous on some interval and $|f|$ is uniformly continuous. Prove or disprove that $f$ is also uniformly continuous.

Published on 09 May 2023 - 14:53

score 34 · Answer 13 · 2023-05-12 19:35:54

34

Views

Examples of continuous but not uniformly continuous functions on various domains

Published on 12 May 2023 - 19:35

score 51 · Answer 14 · 2023-05-21 04:11:51

51

Views

Minimizing direction of a continuous function defined everywhere except at one point and directional limits.

Published on 21 May 2023 - 4:11

score 17 · Answer 15 · 2026-03-14 08:51:18

17

Views

Real analysis / uniformly continuous

Published on 14 Mar 2026 - 8:51

List Question

If I am asked to prove whether or not a function is uniformly continuous, how can I determine whether it is or is not before constructing the proof?

Prove that if $X$ is compact, then every continuous function $f: X \to Y$ is uniformly continuous

Is the Pontryagin map uniformly continuous?

Showing $\displaystyle \lim_{(t_1,t_2) \to (t,t), t_1 < t_2} \frac{\gamma(t_2)-\gamma(t_1)}{t_2-t_1}=\gamma'(t)$ ( using uniform continuity )

How to show function is uniformly continuous over metric spaces.

(Uniform) continuous function $f : [0,\infty) \rightarrow \mathbb R$ is Lebesgue integrable, then $\lim_{x\rightarrow \infty} f(x) =0$?

Is there an analogue of uniform continuity for multivariable functions? And, is addition and multiplication uniformly continuous?

Let $f$ be continuous on an open interval $(a,b)$, and let its limits at $a$ and $b$ exist. Show that $f$ is uniformly continuous on the interval.

What is the space $BUC^s$?

Uniform continuity (in terms of Big-O notation)

$f: (X,d) \rightarrow (X',d')$ uniformly continuous and $A,B \subseteq E: \ d(A,B) = 0 \Rightarrow d'(f(A),f(B))=0$

If $f$ is continuous on some interval and $|f|$ is uniformly continuous. Prove or disprove that $f$ is also uniformly continuous.

Examples of continuous but not uniformly continuous functions on various domains

Minimizing direction of a continuous function defined everywhere except at one point and directional limits.

Real analysis / uniformly continuous

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