Typical property of the topological entropy of continuous mappings of compact sets


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Abstract

We show that the topological entropy viewed as a functional on the space of continuous mappings of a metric compact set into itself with the uniform topology is a function of the second Baire class and is lower semicontinuous at a Baire typical point. In particular, we show that the topological entropy is zero at a Baire typical point of the space of continuous mappings of the Baire space of sequences of zeros and units.

About the authors

A. N. Vetokhin

Russian State University of Tourism and Service

Author for correspondence.
Email: anveto27@yandex.ru
Russian Federation, Cherkizovo, Moscow Region, 141221

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