Topologically inseparable functions I: Finitary case
The present paper is the first of two papers in which the authors study the following problem: Given a finite set \(A\) and a distinguished function \(f:A\to A\), what can we say about the set of all functions \(g:A\to A\) that are continuous for all topologies for which \(f\) is continuous? In their effort to answer the above problem, the authors prove a lot of interesting results and finally show the main result which is a characterization of the functions \(f\) such that this set is trivial, that is, contains only the constant functions and the iterates of \(f\).
scientific article; zbMATH DE number 1883936