Question

Proof $f(x) = x^2$ is uniformly continuous in $[0,17]$

score 84 · Answer 1 · 2017-12-22 12:20:25

84

Views

Proof $f(x) = x^2$ is uniformly continuous in $[0,17]$

Published on 22 Dec 2017 - 12:20

score 366 · Answer 2 · 2017-12-22 13:35:34

366

Views

Uniformly continuous only on compact space

Published on 22 Dec 2017 - 13:35

score 442 · Answer 3 · 2017-12-22 18:26:47

442

Views

Find all $(a,b)$ such that $x^a\sin (x^b)$ uniformly continuous on $(0,1]$.

Published on 22 Dec 2017 - 18:26

score 121 · Answer 4 · 2017-12-22 20:15:58

121

Views

there exists a continuous function $g$ on $\mathbb{R}$ and $\int_{\mathbb{R}}|f-g|<\epsilon$. Can we say that $g$ is uniform

Published on 22 Dec 2017 - 20:15

score 90 · Answer 5 · 2017-12-24 22:28:53

90

Views

Is the mapping $T : x \mapsto \int_{0}^{\bullet} \tau^{-1/2}x(\tau)\,d\tau$ uniformly continuous?

Published on 24 Dec 2017 - 22:28

score 1.6k · Answer 6 · 2026-03-29 13:39:18

1.6k

Views

When every continuous function on a metric space is also uniformly continuous.

Published on 29 Mar 2026 - 13:39

score 1.2k · Answer 7 · 2017-12-31 13:35:26

1.2k

Views

Let $\{f_n\}^\infty_{n=1}$ be a sequence of continuous real valued functions defined on $\mathbb{R}$

Published on 31 Dec 2017 - 13:35

score 2k · Answer 8 · 2018-01-03 12:44:15

2k

Views

Let $f(x): (0,1) \to \mathbb{R} $ be Uniformly continuous. Prove that $f(x)$ is bounded.

Published on 03 Jan 2018 - 12:44

score 634 · Answer 9 · 2018-01-03 13:07:02

634

Views

Uniform Continuity of function $\frac{1}{1+x^2}$

Published on 03 Jan 2018 - 13:07

score 82 · Answer 10 · 2018-01-03 17:13:49

82

Views

Show $F:\Bbb R^n\to \Bbb R$ is uniformly continuous

Published on 03 Jan 2018 - 17:13

score 885 · Answer 11 · 2018-01-05 16:52:27

885

Views

how to prove that $f(x) = \ln (x^2 +1 )$ is not uniform continuous?

Published on 05 Jan 2018 - 16:52

score 806 · Answer 12 · 2026-02-23 17:47:13

806

Views

Is an equicontinuous family of uniformly continuous functions necessarily uniformly equicontinuous?

Published on 23 Feb 2026 - 17:47

score 76 · Answer 13 · 2018-01-06 18:40:25

76

Views

Lipschitz continuity question.

Published on 06 Jan 2018 - 18:40

score 105 · Answer 14 · 2026-03-29 10:55:36

105

Views

Functions on circle equal coincide with exponential

Published on 29 Mar 2026 - 10:55

score 3.4k · Answer 15 · 2018-01-09 18:52:41

3.4k

Views

Prove directly from definition that $\tan(x)$ is not uniformly continuous on $(-\pi/2, \pi/2)$

Published on 09 Jan 2018 - 18:52

List Question

Proof $f(x) = x^2$ is uniformly continuous in $[0,17]$

Uniformly continuous only on compact space

Find all $(a,b)$ such that $x^a\sin (x^b)$ uniformly continuous on $(0,1]$.

there exists a continuous function $g$ on $\mathbb{R}$ and $\int_{\mathbb{R}}|f-g|<\epsilon$. Can we say that $g$ is uniform

Is the mapping $T : x \mapsto \int_{0}^{\bullet} \tau^{-1/2}x(\tau)\,d\tau$ uniformly continuous?

When every continuous function on a metric space is also uniformly continuous.

Let $\{f_n\}^\infty_{n=1}$ be a sequence of continuous real valued functions defined on $\mathbb{R}$

Let $f(x): (0,1) \to \mathbb{R} $ be Uniformly continuous. Prove that $f(x)$ is bounded.

Uniform Continuity of function $\frac{1}{1+x^2}$

Show $F:\Bbb R^n\to \Bbb R$ is uniformly continuous

how to prove that $f(x) = \ln (x^2 +1 )$ is not uniform continuous?

Is an equicontinuous family of uniformly continuous functions necessarily uniformly equicontinuous?

Lipschitz continuity question.

Functions on circle equal coincide with exponential

Prove directly from definition that $\tan(x)$ is not uniformly continuous on $(-\pi/2, \pi/2)$

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