## 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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