Topological nearly entropy

The purpose of this paper is to generalize the notions of Adler’s topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f−1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.