Question

CheckMyProof: $f$ is bounded, uniformly continuous $\implies e^{f}$ is bounded, uniformly cts.

score 280 · Answer 1 · 2026-03-25 06:27:56

280

Views

CheckMyProof: $f$ is bounded, uniformly continuous $\implies e^{f}$ is bounded, uniformly cts.

Published on 25 Mar 2026 - 6:27

score 545 · Answer 2 · 2018-04-10 16:05:03

545

Views

The product of two uniformly continuous functions on $\Bbb R$ don't have to be uniformly continuous

Published on 10 Apr 2018 - 16:05

score 433 · Answer 3 · 2018-04-11 13:49:23

433

Views

Vanishing at infinity implies uniform continuity

Published on 11 Apr 2018 - 13:49

score 66 · Answer 4 · 2018-04-11 23:03:57

66

Views

Uniform continuity of $f(x) = x$ on $\Bbb R$

Published on 11 Apr 2018 - 23:03

score 42 · Answer 5 · 2018-04-14 08:13:32

42

Views

Follow-up question: what if the interval is not (0, 1)? Say (1, 2)?

Published on 14 Apr 2018 - 8:13

score 55 · Answer 6 · 2018-04-15 16:25:24

55

Views

Uniform convergence - is this too easy?

Published on 15 Apr 2018 - 16:25

score 868 · Answer 7 · 2026-03-25 10:53:42

868

Views

The random variable U is uniformly distributed over the interval [3,6]. Find the following probabilities

Published on 25 Mar 2026 - 10:53

score 109 · Answer 8 · 2018-04-18 14:05:11

109

Views

Let $f: \Bbb R \to \Bbb R$ be such that $|f(x) -f(y)| \le |x - y |^2 \ \forall \ x,\ y \in \Bbb R$. How can I show that $f$ is constant?

Published on 18 Apr 2018 - 14:05

score 91 · Answer 9 · 2026-03-25 02:02:53

91

Views

Lipschitzian function implies uniformly continuity - choice of delta

Published on 25 Mar 2026 - 2:02

score 321 · Answer 10 · 2018-04-18 20:43:18

321

Views

For what value of $n \in \Bbb N$ the function $f(x)=x^n$ is uniformly continuous in all of the set $\Bbb R$

Published on 18 Apr 2018 - 20:43

score 78 · Answer 11 · 2026-03-25 08:10:00

78

Views

Proving that $f(x)=x^2$ is uniformly continuous on any closed interval, but not on $\mathbb{R}$

Published on 25 Mar 2026 - 8:10

score 1.3k · Answer 12 · 2026-03-25 04:40:12

1.3k

Views

Uniformly continuous functions and the preservation of Cauchy sequences

Published on 25 Mar 2026 - 4:40

score 1.4k · Answer 13 · 2018-04-23 08:59:58

1.4k

Views

Proof Verification/Doubt: Showing $f(x)=1/x^2$ is not uniformly continuous on $(0,\infty)$

Published on 23 Apr 2018 - 8:59

score 3.3k · Answer 14 · 2026-03-24 22:10:49

3.3k

Views

Hölder continuous functions are uniformly continuous

Published on 24 Mar 2026 - 22:10

score 347 · Answer 15 · 2026-03-25 08:05:53

347

Views

Showing that a function is Uniformly continuous

Published on 25 Mar 2026 - 8:05

List Question

CheckMyProof: $f$ is bounded, uniformly continuous $\implies e^{f}$ is bounded, uniformly cts.

The product of two uniformly continuous functions on $\Bbb R$ don't have to be uniformly continuous

Vanishing at infinity implies uniform continuity

Uniform continuity of $f(x) = x$ on $\Bbb R$

Follow-up question: what if the interval is not (0, 1)? Say (1, 2)?

Uniform convergence - is this too easy?

The random variable U is uniformly distributed over the interval [3,6]. Find the following probabilities

Let $f: \Bbb R \to \Bbb R$ be such that $|f(x) -f(y)| \le |x - y |^2 \ \forall \ x,\ y \in \Bbb R$. How can I show that $f$ is constant?

Lipschitzian function implies uniformly continuity - choice of delta

For what value of $n \in \Bbb N$ the function $f(x)=x^n$ is uniformly continuous in all of the set $\Bbb R$

Proving that $f(x)=x^2$ is uniformly continuous on any closed interval, but not on $\mathbb{R}$

Uniformly continuous functions and the preservation of Cauchy sequences

Proof Verification/Doubt: Showing $f(x)=1/x^2$ is not uniformly continuous on $(0,\infty)$

Hölder continuous functions are uniformly continuous

Showing that a function is Uniformly continuous

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