PreprintCC BY-NC-ND 4.0arXiv
Characterization of sets in metric spaces where the big Lipschitz derivative is infinite
Abstract
Let X be a metric space without isolated points. In this paper we prove that E is a Gδ-set in X if and only if there exists a continuous function f:X→ℝ whose big Lipschitz derivative is infinite precisely on E. To this end, we introduce a new generalization of the classical Takagi function to the setting of metric spaces.
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BibTeX
@misc{llorente2026characterization,
title = {{Characterization of sets in metric spaces where the big Lipschitz derivative is infinite}},
author = {Jesús Llorente and Oleksandr Maslyuchenko and Ziemowit Wójcicki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38856},
eprint = {2610.38856},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38856},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Characterization of sets in metric spaces where the big Lipschitz derivative is infinite
AU - Jesús Llorente
AU - Oleksandr Maslyuchenko
AU - Ziemowit Wójcicki
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38856
UR - https://arxiv.org/abs/2610.38856
AB - Let X be a metric space without isolated points. In this paper we prove that E is a G_δ-set in X if and only if there exists a continuous function f:X→ℝ whose big Lipschitz derivative is infinite precisely on E. To this end, we introduce a new generalization of the classical Takagi function to the setting of metric spaces.
ER -