Question

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

score 282 · Answer 1 · 2026-04-12 12:55:27

282

Views

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

Published on 12 Apr 2026 - 12:55

score 548 · Answer 2 · 2026-04-11 00:45:23

548

Views

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

Published on 11 Apr 2026 - 0:45

score 435 · Answer 3 · 2026-04-15 05:43:16

435

Views

Vanishing at infinity implies uniform continuity

Published on 15 Apr 2026 - 5:43

score 69 · Answer 4 · 2026-04-15 03:33:27

69

Views

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

Published on 15 Apr 2026 - 3:33

score 45 · Answer 5 · 2026-04-15 20:30:04

45

Views

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

Published on 15 Apr 2026 - 20:30

score 58 · Answer 6 · 2026-04-16 07:38:54

58

Views

Uniform convergence - is this too easy?

Published on 16 Apr 2026 - 7:38

score 869 · Answer 7 · 2026-04-15 08:43:32

869

Views

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

Published on 15 Apr 2026 - 8:43

score 112 · Answer 8 · 2026-04-15 04:49:27

112

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 15 Apr 2026 - 4:49

score 93 · Answer 9 · 2026-04-12 05:49:22

93

Views

Lipschitzian function implies uniformly continuity - choice of delta

Published on 12 Apr 2026 - 5:49

score 324 · Answer 10 · 2026-04-14 21:51:10

324

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 14 Apr 2026 - 21:51

score 80 · Answer 11 · 2026-04-12 23:48:34

80

Views

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

Published on 12 Apr 2026 - 23:48

score 1.3k · Answer 12 · 2026-04-12 04:29:24

1.3k

Views

Uniformly continuous functions and the preservation of Cauchy sequences

Published on 12 Apr 2026 - 4:29

score 1.4k · Answer 13 · 2026-04-14 02:22:15

1.4k

Views

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

Published on 14 Apr 2026 - 2:22

score 3.4k · Answer 14 · 2026-05-10 13:45:50

3.4k

Views

Hölder continuous functions are uniformly continuous

Published on 10 May 2026 - 13:45

score 349 · Answer 15 · 2026-04-09 13:41:00

349

Views

Showing that a function is Uniformly continuous

Published on 09 Apr 2026 - 13:41

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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