Narrow Results

We introduce and study the topological concepts of entropy points, expansivity and shadowing property for dynamical systems on noncompact nonmetrizable spaces, which generalize the relevant concepts for metric spaces. We also obtain various properties on uniform entropy on noncompact nonmetrizable spaces. The main result is a theorem which yields a relation between topological shadowing property and positive uniform entropy.

We give a sufficient condition for sensitivity of continuous maps defined on a uniform space. We also study property $P$ for uniformly continuous maps defined on a uniform space and its relation with uniform entropy.