In the recent decade, different extensions of Shannon entropy have been introduced. One of them which generalizes many classical entropies is unified (r, s)-entropy. The properties of topological entropy and Shannon entropy are similar. In this paper, we extend the concept of unified (r, s)-entropy to the topological dynamical system by using Bowen’s definition of separated and spanning sets. We call this notion topological Unified (r, s)-entropy. Then we find the value of topological unified (r, s)-entropy when X is a noncompact metric space and get the value of the topological unified (r, s)-entropy for X∗ when X∗ is one point-compactification of X.

Keywords