Lipschitz continuous points of functions on an interval

In this paper, we address the problem of finding functions with predetermined Lipschitz continuous points. More precisely, given A⊆[0,1], we are interested in the existence of function f:[0,1]→R which is Lipschitz continuous exactly on A. Our result is related to Liouville numbers.

Saved in:
Bibliographic Details
Published inExamples and counterexamples Vol. 8; p. 100194
Main Author Shen, Zhekai
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Elsevier
Subjects
Liouville numbers
Lipschitz continuous
Oscillation functions
Lipschitz continuous
Oscillation functions
Liouville numbers
Online AccessGet full text
ISSN2666-657X
2666-657X
DOI10.1016/j.exco.2025.100194

Cover

More Information
Summary:In this paper, we address the problem of finding functions with predetermined Lipschitz continuous points. More precisely, given A⊆[0,1], we are interested in the existence of function f:[0,1]→R which is Lipschitz continuous exactly on A. Our result is related to Liouville numbers.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2025.100194