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

2026/07/30 by Jan Dudák
Mathematics · #math.FA #math.CA #msc:46B87

paper · pdf

9 pages, 2 figures

arxiv created 2026/07/30 · arxiv updated 2026/07/31

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.

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