Question

Are uniformly equivalent metrics with the same bounded sets strongly equivalent?

score 336 · Answer 1 · 2026-02-23 01:03:37

336

Views

Are uniformly equivalent metrics with the same bounded sets strongly equivalent?

Published on 23 Feb 2026 - 1:03

score 144 · Answer 2 · 2018-12-23 19:23:14

144

Views

If $f$ is $C^{1}$ and $\sup_{x \in \mathbb{R}}|f'(x)| = \infty$ , prove that $f$ cannot be uniformly continuous

Published on 23 Dec 2018 - 19:23

score 130 · Answer 3 · 2026-03-25 09:23:22

130

Views

Do strongly equivalent metrics have the same covering numbers?

Published on 25 Mar 2026 - 9:23

score 124 · Answer 4 · 2018-12-25 22:00:37

124

Views

Can a Lipschitz continuous function be linear almost everywhere but not linear everywhere?

Published on 25 Dec 2018 - 22:00

score 83 · Answer 5 · 2018-12-26 08:11:01

83

Views

A Lipschitz function must has a set of intervals s.t. $\cup_kI_k=\mathbb R$ and $f$ is either convex or concave on either $I_k$?

Published on 26 Dec 2018 - 8:11

score 682 · Answer 6 · 2018-12-26 22:49:49

682

Views

Lipschitz constant for a second order nonlinear differential equation

Published on 26 Dec 2018 - 22:49

score 122 · Answer 7 · 2026-03-25 07:40:37

122

Views

Example of a nowhere differentiable contraction mapping

Published on 25 Mar 2026 - 7:40

score 258 · Answer 8 · 2019-01-02 15:30:37

258

Views

How can $\ln(x+2)$ have a fixed point in $(-2,-1]$?

Published on 02 Jan 2019 - 15:30

score 37 · Answer 9 · 2019-01-03 13:18:32

37

Views

Showing that the system of a planar curve is Lipschitz in y

Published on 03 Jan 2019 - 13:18

score 903 · Answer 10 · 2019-01-05 14:29:39

903

Views

Prove that $f(x)=x\sin(1/x)$ for $x\ne0$, $f(0)=0$, is not Lipschitz on $[0,1]$

Published on 05 Jan 2019 - 14:29

score 424 · Answer 11 · 2019-01-05 15:11:12

424

Views

Prove or disprove that there exists $K$ such that $|f(x)-f(y)|\leq K |x-y|,\;\forall\;\;x,y\in[0,1],$ edited version.

Published on 05 Jan 2019 - 15:11

score 82 · Answer 12 · 2026-03-25 12:47:32

82

Views

Weak differentiability vs differentiability almost everywhere

Published on 25 Mar 2026 - 12:47

score 301 · Answer 13 · 2019-01-05 21:43:25

301

Views

Lipschitz continuity of $e^{\sin}$

Published on 05 Jan 2019 - 21:43

score 37 · Answer 14 · 2026-02-23 04:56:27

37

Views

Deriving an inequality for a set of functions that have equi-Lipschitz first derivatives.

Published on 23 Feb 2026 - 4:56

score 50 · Answer 15 · 2019-01-12 20:45:33

50

Views

Showing $\{f(\frac{1}{n+1})\}$ converges in $\mathbb{R}$

Published on 12 Jan 2019 - 20:45

List Question

Are uniformly equivalent metrics with the same bounded sets strongly equivalent?

If $f$ is $C^{1}$ and $\sup_{x \in \mathbb{R}}|f'(x)| = \infty$ , prove that $f$ cannot be uniformly continuous

Do strongly equivalent metrics have the same covering numbers?

Can a Lipschitz continuous function be linear almost everywhere but not linear everywhere?

A Lipschitz function must has a set of intervals s.t. $\cup_kI_k=\mathbb R$ and $f$ is either convex or concave on either $I_k$?

Lipschitz constant for a second order nonlinear differential equation

Example of a nowhere differentiable contraction mapping

How can $\ln(x+2)$ have a fixed point in $(-2,-1]$?

Showing that the system of a planar curve is Lipschitz in y

Prove that $f(x)=x\sin(1/x)$ for $x\ne0$, $f(0)=0$, is not Lipschitz on $[0,1]$

Prove or disprove that there exists $K$ such that $|f(x)-f(y)|\leq K |x-y|,\;\forall\;\;x,y\in[0,1],$ edited version.

Weak differentiability vs differentiability almost everywhere

Lipschitz continuity of $e^{\sin}$

Deriving an inequality for a set of functions that have equi-Lipschitz first derivatives.

Showing $\{f(\frac{1}{n+1})\}$ converges in $\mathbb{R}$

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