Question

True/False: properties of a continuous map $f: S^1 \to \Bbb R$.

score 250 · Answer 1 · 2015-12-14 16:42:40

250

Views

True/False: properties of a continuous map $f: S^1 \to \Bbb R$.

Published on 14 Dec 2015 - 16:42

score 1.1k · Answer 2 · 2015-12-15 03:21:59

1.1k

Views

Continuous real valued function that is zero on integers

Published on 15 Dec 2015 - 3:21

score 3.1k · Answer 3 · 2015-12-15 15:11:44

3.1k

Views

Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?

Published on 15 Dec 2015 - 15:11

score 2.1k · Answer 4 · 2015-12-17 00:40:45

2.1k

Views

Uniform boundedness implies equicontinuity on compact domains?

Published on 17 Dec 2015 - 0:40

score 193 · Answer 5 · 2015-12-17 17:34:40

193

Views

Is $f(x)=x\sin(x^{-2})$ uniformly continuous on (0,1)? Is $f(x)=\sin(x^{-2})$?

Published on 17 Dec 2015 - 17:34

score 116 · Answer 6 · 2015-12-18 17:36:00

116

Views

Using Bounded Derivative to Show Uniform Continuity

Published on 18 Dec 2015 - 17:36

score 71 · Answer 7 · 2015-12-19 21:03:05

71

Views

Show that $\sqrt{x^2 +1 }$ is uniformly continuous. $x \in \mathbb{R}$

Published on 19 Dec 2015 - 21:03

score 159 · Answer 8 · 2015-12-20 04:16:31

159

Views

Alternative way to show $f(x) = x^2$ is uniformly continuous in a fixed closed interval

Published on 20 Dec 2015 - 4:16

score 1.5k · Answer 9 · 2015-12-21 08:38:57

1.5k

Views

Let $f: \Bbb R \to \Bbb R$ be a differentiable function such that $\sup_{x \in \Bbb R}|f'(x)| \lt \infty$. Then

Published on 21 Dec 2015 - 8:38

score 127 · Answer 10 · 2015-12-23 10:38:31

127

Views

Suppose $f : X \to Y$ is a (continuous) bounded map.Does this implies that $f$ is uniformly continuous?

Published on 23 Dec 2015 - 10:38

score 482 · Answer 11 · 2026-03-28 11:35:07

482

Views

A function given as an integral is uniformly continuous provided the integrand is uniformly continuous

Published on 28 Mar 2026 - 11:35

score 870 · Answer 12 · 2015-12-30 01:19:35

870

Views

Is a continuous function between two uniformly continuous functions uniformly continuous?

Published on 30 Dec 2015 - 1:19

score 3.8k · Answer 13 · 2016-01-02 03:27:00

3.8k

Views

Assume that $ f: R \to R $ is uniformly continuous. prove that there are constants A,B such that $ |f(x)| \le A + B|x| $ for all $ x \in R $.

Published on 02 Jan 2016 - 3:27

score 86 · Answer 14 · 2016-01-03 08:38:55

86

Views

Prove that $\phi : C[a,b]\rightarrow \mathbb{R}$ given by $\phi(f)=\int_a^bfdx$ is uniformly continuous

Published on 03 Jan 2016 - 8:38

score 268 · Answer 15 · 2016-01-05 16:12:33

268

Views

Using the epsilon-delta definition, show that $\tan x$ is not uniformly continuous on $\left[0, \frac{\pi}{2} \right)$.

Published on 05 Jan 2016 - 16:12

List Question

True/False: properties of a continuous map $f: S^1 \to \Bbb R$.

Continuous real valued function that is zero on integers

Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?

Uniform boundedness implies equicontinuity on compact domains?

Is $f(x)=x\sin(x^{-2})$ uniformly continuous on (0,1)? Is $f(x)=\sin(x^{-2})$?

Using Bounded Derivative to Show Uniform Continuity

Show that $\sqrt{x^2 +1 }$ is uniformly continuous. $x \in \mathbb{R}$

Alternative way to show $f(x) = x^2$ is uniformly continuous in a fixed closed interval

Let $f: \Bbb R \to \Bbb R$ be a differentiable function such that $\sup_{x \in \Bbb R}|f'(x)| \lt \infty$. Then

Suppose $f : X \to Y$ is a (continuous) bounded map.Does this implies that $f$ is uniformly continuous?

A function given as an integral is uniformly continuous provided the integrand is uniformly continuous

Is a continuous function between two uniformly continuous functions uniformly continuous?

Assume that $ f: R \to R $ is uniformly continuous. prove that there are constants A,B such that $ |f(x)| \le A + B|x| $ for all $ x \in R $.

Prove that $\phi : C[a,b]\rightarrow \mathbb{R}$ given by $\phi(f)=\int_a^bfdx$ is uniformly continuous

Using the epsilon-delta definition, show that $\tan x$ is not uniformly continuous on $\left[0, \frac{\pi}{2} \right)$.

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