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

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.