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Entropies of self-mappings of topological spaces with richer structures

Miroslav Katětov — 1993

Commentationes Mathematicae Universitatis Carolinae

For mappings f : S S , where S is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the δ -entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the δ -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 δ -entropy of f : S S .

Entropy-like functionals: conceptual background and some results

Miroslav Katětov — 1992

Commentationes Mathematicae Universitatis Carolinae

We describe a conceptual approach which provides a unified view of various entropy-like functionals on the class of semimetric spaces, endowed with a bounded measure. The entropy E considered in the author’s previous articles is modified so as to assume finite values for a fairly wide class of spaces which fail to be totally bounded.

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