Question

Rigorous proof for the converse of $\lim_{x \to \infty} f(x) \implies f $ is uniformly continuous

score 70 · Answer 1 · 2021-12-01 09:51:13

70

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Rigorous proof for the converse of $\lim_{x \to \infty} f(x) \implies f $ is uniformly continuous

Published on 01 Dec 2021 - 9:51

score 68 · Answer 2 · 2021-12-03 00:04:35

68

Views

Show that if $f \in L^1 \cap C$, then $\sum_{n \in \mathbb{Z}} f(x+n)$ exists and is uniformly continuous

Published on 03 Dec 2021 - 0:04

score 198 · Answer 3 · 2021-12-03 21:46:56

198

Views

Disproving uniform continuity of $x^n$ on [0,1].

Published on 03 Dec 2021 - 21:46

score 64 · Answer 4 · 2026-02-24 05:07:52

64

Views

Necessary and suficient condition for a uniform space to be complete

Published on 24 Feb 2026 - 5:07

score 862 · Answer 5 · 2021-12-09 19:11:30

862

Views

Is it true that, if $f$ is uniformly continuous in $(a,b),$ then the limits $\lim_{x\to a^+} f(x)$ and $\lim_{x\to b^-} f(x)$ exist?

Published on 09 Dec 2021 - 19:11

score 83 · Answer 6 · 2021-12-20 14:55:32

83

Views

Function that is defined for all reals and is continuous but not uniformly continuous

Published on 20 Dec 2021 - 14:55

score 134 · Answer 7 · 2021-12-27 11:52:28

134

Views

Continuity at the boundary of a convergent power series

Published on 27 Dec 2021 - 11:52

score 248 · Answer 8 · 2026-03-30 10:19:54

248

Views

Uniformly continuous function on totally bounded subset of complete metric space

Published on 30 Mar 2026 - 10:19

score 191 · Answer 9 · 2022-01-06 20:31:53

191

Views

Is a right-continuous function on a compact space even "uniformly right-continuous"?

Published on 06 Jan 2022 - 20:31

score 951 · Answer 10 · 2022-01-09 17:54:30

951

Views

Is $f(x) = 1/x$ over $[0.1 , 1]$ uniformly continuous but $1/x$ on $(0,1)$ is not?

Published on 09 Jan 2022 - 17:54

score 81 · Answer 11 · 2022-01-17 09:59:57

81

Views

Wikipedia says that a function is uniformly continuous if and only if it admits a modulus of continuity.

Published on 17 Jan 2022 - 9:59

score 105 · Answer 12 · 2022-01-18 17:01:15

105

Views

The confusion about the proof of if function is continuous on a closed interval $[a,b]$,then it is integrable

Published on 18 Jan 2022 - 17:01

score 108 · Answer 13 · 2022-01-19 01:30:05

108

Views

A bounded, continuous and monotone function must be uniformly continuous on an open interval

Published on 19 Jan 2022 - 1:30

score 88 · Answer 14 · 2022-01-26 00:45:05

88

Views

$f:[a,\infty) \longrightarrow \mathbb{R}$ continuous and $\lim_{x\to \infty}{f(x)}=c\in \mathbb{R}$ so $f$ is uniformly continuos in $[a,\infty)$

Published on 26 Jan 2022 - 0:45

score 140 · Answer 15 · 2022-01-26 21:57:09

140

Views

A function $f(x)$ is uniformly continuous on $(a,b)$ $\iff$ it can be defined on $\{a, b\}$ such that $f$ is continuous on $[a,b]$.

Published on 26 Jan 2022 - 21:57

List Question

Rigorous proof for the converse of $\lim_{x \to \infty} f(x) \implies f $ is uniformly continuous

Show that if $f \in L^1 \cap C$, then $\sum_{n \in \mathbb{Z}} f(x+n)$ exists and is uniformly continuous

Disproving uniform continuity of $x^n$ on [0,1].

Necessary and suficient condition for a uniform space to be complete

Is it true that, if $f$ is uniformly continuous in $(a,b),$ then the limits $\lim_{x\to a^+} f(x)$ and $\lim_{x\to b^-} f(x)$ exist?

Function that is defined for all reals and is continuous but not uniformly continuous

Continuity at the boundary of a convergent power series

Uniformly continuous function on totally bounded subset of complete metric space

Is a right-continuous function on a compact space even "uniformly right-continuous"?

Is $f(x) = 1/x$ over $[0.1 , 1]$ uniformly continuous but $1/x$ on $(0,1)$ is not?

Wikipedia says that a function is uniformly continuous if and only if it admits a modulus of continuity.

The confusion about the proof of if function is continuous on a closed interval $[a,b]$,then it is integrable

A bounded, continuous and monotone function must be uniformly continuous on an open interval

$f:[a,\infty) \longrightarrow \mathbb{R}$ continuous and $\lim_{x\to \infty}{f(x)}=c\in \mathbb{R}$ so $f$ is uniformly continuos in $[a,\infty)$

A function $f(x)$ is uniformly continuous on $(a,b)$ $\iff$ it can be defined on $\{a, b\}$ such that $f$ is continuous on $[a,b]$.

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