Alder's topological entropy of generalized discrete dynamical system

The purpose of this paper is to introduce the topological entropy for so called generalized discrete dynamical system; this is achieved through the consideration of open cover for generalized discrete dynamical system. Besides, we pursue that our definition keeps some properties which are hold by the classic definition of topological entropy introduced for compact sets. These results further extend the scope of the research on discrete dynamical system and generalize the existing results to a very general case.