Entropies of self-mappings of topological spaces with richer structures. (English) Zbl 0839.54022

Katětov, Miroslav

Commentat. Math. Univ. Carol. 34, No. 4, 747-768 (1993).

Summary: For mappings \(f : S \to S\), where \(S\) is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the \(\delta\)-entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the \(\delta\)-entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of \(S^N\), which is closely connected with the \(\delta\)-entropy of \(f : S \to S\).

MSC:

54C70	Entropy in general topology
54E17	Nearness spaces

Keywords:

merotopic space; diameter function; topological entropy; entropy of self-mappings