On a problem of Eidelheit from {\tt The Scottish Book} concerning absolutely continuous functions

TL;DR

This paper provides a negative solution to Eidelheit's problem on superpositions of separately absolutely continuous functions, discusses related problems, and explains the results using Banach space embeddings.

Contribution

It presents the first negative solution to Eidelheit's problem and offers a Banach space perspective on these negative results.

Findings

Negative solution to Eidelheit's Problem 188

Analysis of related problems with similar negative outcomes

Explanation of results via Banach space embeddings

Abstract

A negative solution of Problem 188 posed by Max Eidelheit in {\it the Scottish Book} concerning superpositions of separately absolutely continuous functions is presented. We discuss here his and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the "embeddings of Banach spaces" point of view.