Topological Pseudo Orbit Tracing Property, Topological Sensitivity and Topological Entropy

Abstract

We introduce and study pseudo orbit tracing property on general topological spaces termed as topological pseudo orbit tracing property. We prove that on a compact Hausdorff space, a topologically sensitive dynamical system having topological pseudo orbit tracing property is cofinitely topologically sensitive and has positive topological entropy. Moreover, we also prove that such a dynamical system is locally uncountable.