Topological Entropy, Entropy points and shadowing
  In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having shadowing property. 
Seyyed Alireza Ahmadi
math.DS