A note on uniform entropy for maps having topological specification property

Abstract

We prove that if a uniformly continuous self-map $f$ of a uniform space has topological specification property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided to justify that the converse is not true.

Keywords

• topological specification property
• uniform entropy
• uniform spaces.