Embedding $C(K)$ for countable $K$ into $C([0,1])$ as Besicovitch functions

Jan Dudák

Embedding $C(K)$ for countable $K$ into $C([0,1])$ as Besicovitch functions

Functional Analysis 2026-07-30 v1 Classical Analysis and ODEs

Authors: Jan Dudák

Abstract

Extending a recent result from [Bull. Belg. Math. Soc. Simon Stevin 33 (2026), 138-144], we prove that the space of continuous functions $C(X)$ on any countable compact space $X$ admits an isometric copy in $C([0,1])$ consisting, except for the zero function, entirely of Besicovitch functions, i.e., functions that have no one-sided derivative (finite or infinite) at any point.

Cite

@article{arxiv.2607.28038,
  title  = {Embedding $C(K)$ for countable $K$ into $C([0,1])$ as Besicovitch functions},
  author = {Jan Dudák},
  journal= {arXiv preprint arXiv:2607.28038},
  year   = {2026}
}

Comments

9 pages, 2 figures