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

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
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