Additivity of local function and dynamical system

The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering some generalized open sets. In this situation some of the properties of local function fails to hold due to the finite intersection property of the topology. Due to this outcome, we are investigating the situation of dynamical system and Topological Transitivity.