Question

Real Analysis - Equivalence of uniform continuity of a uniform function when 3 properties are met.

score 37 · Answer 1 · 2023-05-22 17:59:52

37

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Real Analysis - Equivalence of uniform continuity of a uniform function when 3 properties are met.

Published on 22 May 2023 - 17:59

score 110 · Answer 2 · 2023-05-23 13:20:02

110

Views

Is $y=x^{1/3}$ uniformly continuous on $[-1,1]$?

Published on 23 May 2023 - 13:20

score 103 · Answer 3 · 2023-05-25 11:48:23

103

Views

$g(x)=\int_{(-\infty,x)} f d\lambda,$ where $f:\mathbb R\to \mathbb R$ is integrable, is uniformly continuous on $\mathbb R$.

Published on 25 May 2023 - 11:48

score 142 · Answer 4 · 2023-06-01 06:46:50

142

Views

Prove that $f(x) = \frac{1}{\sin(x)}$ is not uniformly continuous on $(0, \pi)$

Published on 01 Jun 2023 - 6:46

score 73 · Answer 5 · 2023-06-03 15:22:57

73

Views

Let $A$ be some interval and $f,g: A \to \mathbb R$. Assume $f,g$ are uniformly continuous and bounded. Prove/disprove $fg$ is uniformly continuous.

Published on 03 Jun 2023 - 15:22

score 182 · Answer 6 · 2023-06-09 06:10:05

182

Views

Is "uniform continuity theorem" provable without using sequences?

Published on 09 Jun 2023 - 6:10

score 95 · Answer 7 · 2023-06-14 03:21:04

95

Views

Riemann integral and uniform continuity

Published on 14 Jun 2023 - 3:21

score 107 · Answer 8 · 2023-06-18 16:25:07

107

Views

Is it possible to find a universal $\delta_U$, such that $|x-y|<\delta_U\Longrightarrow |f_n(x)-f_n(y)|<\epsilon, \forall n=\color{red}0,1,2\dots$

Published on 18 Jun 2023 - 16:25

score 31 · Answer 9 · 2023-06-20 09:49:18

31

Views

Uniform limit theorem for arbitrary uniform space.

Published on 20 Jun 2023 - 9:49

score 99 · Answer 10 · 2026-03-27 14:55:15

99

Views

I don't understand one of the steps in proving that a Uniformly Continuous Function can be extended in a metric space.

Published on 27 Mar 2026 - 14:55

score 123 · Answer 11 · 2023-06-25 21:40:56

123

Views

Proof that $x^2$ is not uniformly continuous on $\mathbb{R}$

Published on 25 Jun 2023 - 21:40

score 27 · Answer 12 · 2023-06-26 11:35:28

27

Views

Uniform continuity subtlety

Published on 26 Jun 2023 - 11:35

score 44 · Answer 13 · 2023-06-28 09:21:48

44

Views

Continuous on $\left[0,\infty\right)$ with limit implies uniform continuous

Published on 28 Jun 2023 - 9:21

score 48 · Answer 14 · 2023-07-02 05:13:18

48

Views

A question about spaces of continous function.

Published on 02 Jul 2023 - 5:13

score 256 · Answer 15 · 2023-07-11 07:17:22

256

Views

Prove $\cos{\sqrt{x}}$ is uniformly continuous, $x \in [0,+\infty)$

Published on 11 Jul 2023 - 7:17

List Question

Real Analysis - Equivalence of uniform continuity of a uniform function when 3 properties are met.

Is $y=x^{1/3}$ uniformly continuous on $[-1,1]$?

$g(x)=\int_{(-\infty,x)} f d\lambda,$ where $f:\mathbb R\to \mathbb R$ is integrable, is uniformly continuous on $\mathbb R$.

Prove that $f(x) = \frac{1}{\sin(x)}$ is not uniformly continuous on $(0, \pi)$

Let $A$ be some interval and $f,g: A \to \mathbb R$. Assume $f,g$ are uniformly continuous and bounded. Prove/disprove $fg$ is uniformly continuous.

Is "uniform continuity theorem" provable without using sequences?

Riemann integral and uniform continuity

Is it possible to find a universal $\delta_U$, such that $|x-y|<\delta_U\Longrightarrow |f_n(x)-f_n(y)|<\epsilon, \forall n=\color{red}0,1,2\dots$

Uniform limit theorem for arbitrary uniform space.

I don't understand one of the steps in proving that a Uniformly Continuous Function can be extended in a metric space.

Proof that $x^2$ is not uniformly continuous on $\mathbb{R}$

Uniform continuity subtlety

Continuous on $\left[0,\infty\right)$ with limit implies uniform continuous

A question about spaces of continous function.

Prove $\cos{\sqrt{x}}$ is uniformly continuous, $x \in [0,+\infty)$

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