## Miroslav Kat\v etov

*Entropies of self-mappings of topological spaces with richer structures *

Comment.Math.Univ.Carolinae 34,4 (1993) 747-768. **Abstract:**For mappings $f : S\rightarrow S$, 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 $f : S\rightarrow S$.

**Keywords:** entropy, merotopic space, self-mapping, diameter function

**AMS Subject Classification:** 54C70, 54E17

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