Topologically inseparable functions II: Infinitary case
The present paper is the second of a two part paper. The author studies the set of all functions \(g:A\to A\) that are continuous for all topologies for which a function \(f:A\to A\) \((A\) is an infinite set) is continuous (while in the first paper the given set \(A\) is finite). The paper is divided in two main sections. In the first part the author restricts his attention to unary functions topologically inseparable from \(f\). In the last part the author studies the clone of finitary functions inseparable from \(f\). The main result of this paper is that if \(f\) is infinitary, then the set \(S(A,f)= \{g:A\to A:g\) is continuous for all topologies for which \(f\) is continuous\} coincides with the set which contains only the constant functions and the iterates of \(f\).
scientific article; zbMATH DE number 1883937