Question

Is the Composition of Lipschitz Continuous Functions Lipschitz Continuous in the Limit to $\infty$

score 8.4k · Answer 1 · 2026-03-24 22:51:05

8.4k

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Is the Composition of Lipschitz Continuous Functions Lipschitz Continuous in the Limit to $\infty$

Published on 24 Mar 2026 - 22:51

score 628 · Answer 2 · 2018-03-16 17:52:14

628

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Proving a function is discontinuous by constructing a sequence

Published on 16 Mar 2018 - 17:52

score 41 · Answer 3 · 2026-03-25 01:23:53

41

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Functional Analysis - Set of Applications is Open and Closed

Published on 25 Mar 2026 - 1:23

score 1k · Answer 4 · 2018-03-17 08:35:39

1k

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Confusion in Oscillatory Discontinuity - A Peculiar Example

Published on 17 Mar 2018 - 8:35

score 50 · Answer 5 · 2018-03-17 13:51:05

50

Views

Product Topology/Continuity Confusion

Published on 17 Mar 2018 - 13:51

score 80 · Answer 6 · 2026-03-25 00:24:27

80

Views

How to decide the neighbourhood when proving a function is locally Lipschitz-continuous.

Published on 25 Mar 2026 - 0:24

score 605 · Answer 7 · 2026-03-25 03:18:16

605

Views

Proving discontinuity using $\epsilon$-$\delta$ form

Published on 25 Mar 2026 - 3:18

score 30 · Answer 8 · 2026-03-27 13:20:19

30

Views

Searching for tricks or quick techniques to identify if $f_n$ (or $f'_n$) is continuous but $f$ (or $f'$) is not continuous.

Published on 27 Mar 2026 - 13:20

score 437 · Answer 9 · 2026-03-25 11:01:03

437

Views

Exercise 4.13 from Rudin, what's wrong with this proof.

Published on 25 Mar 2026 - 11:01

score 303 · Answer 10 · 2026-03-25 11:00:04

303

Views

How to determine if a continuous function is uniformly continuous

Published on 25 Mar 2026 - 11:00

score 103 · Answer 11 · 2018-03-18 15:28:19

Continuity of the function $f(x)=\begin{cases} 3,\text{ if }0\leq x\leq1\\ 4,\text{ if }1< x<3\\ 5,\text{ if }3\leq x\leq10\\ \end{cases}$

score 395 · Answer 12 · 2018-03-19 11:36:05

395

Views

Doubt in proof of Convex Function Continuous

Published on 19 Mar 2018 - 11:36

score 199 · Answer 13 · 2018-03-19 17:17:30

199

Views

Discontinuity of $\sin(\frac{1}{x})$

Published on 19 Mar 2018 - 17:17

score 81 · Answer 14 · 2018-03-19 20:15:27

81

Views

Proving some statements, given that $|f(x)-f(y)| \leq M|x-y|^{\alpha}$

Published on 19 Mar 2018 - 20:15

score 109 · Answer 15 · 2018-03-19 20:43:25

109

Views

Proving this log function is continuous

Published on 19 Mar 2018 - 20:43

List Question

Is the Composition of Lipschitz Continuous Functions Lipschitz Continuous in the Limit to $\infty$

Proving a function is discontinuous by constructing a sequence

Functional Analysis - Set of Applications is Open and Closed

Confusion in Oscillatory Discontinuity - A Peculiar Example

Product Topology/Continuity Confusion

How to decide the neighbourhood when proving a function is locally Lipschitz-continuous.

Proving discontinuity using $\epsilon$-$\delta$ form

Searching for tricks or quick techniques to identify if $f_n$ (or $f'_n$) is continuous but $f$ (or $f'$) is not continuous.

Exercise 4.13 from Rudin, what's wrong with this proof.

How to determine if a continuous function is uniformly continuous

Continuity of the function $f(x)=\begin{cases} 3,\text{ if }0\leq x\leq1\\ 4,\text{ if }1< x<3\\ 5,\text{ if }3\leq x\leq10\\ \end{cases}$

Doubt in proof of Convex Function Continuous

Discontinuity of $\sin(\frac{1}{x})$

Proving some statements, given that $|f(x)-f(y)| \leq M|x-y|^{\alpha}$

Proving this log function is continuous

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