Embedding for countable into as Besicovitch functions
arXiv:2607.28038
summary
The paper shows that for any countable compact space X, the Banach space C(X) can be embedded isometrically into C([0,1]) so that, apart from the zero function, all functions in the image are Besicovitch functions—functions lacking any one‑sided derivative at every point.
Abstract
Extending a recent result from [Bull. Belg. Math. Soc. Simon Stevin 33 (2026), 138-144], we prove that the space of continuous functions on any countable compact space admits an isometric copy in 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.
9 pages, 2 figures
Topics & keywords
#continuous functions#isometric embedding#Besicovitch functions#countable compact spaces#Banach spacesC(K)C([0,1])isometric copyone-sided derivativeBesicovitch functioncountable compact