Smooth topological spaces

SUMMARY Smooth Topological Spaces The study entitled "Smooth Topological Spaces" consists of two chapters. In the first chapter, füdamental concepts and theorems used in the study are explored. The second chapter includes some studies related to smooth topological spaces. In this study, the concepts of smooth compactness types, connectedness and the grading of separating axioms which some researchers defined differently from different points of view were given and some of their relatedness with each other were studied. From the studies examined, we tried to prove that there are substantially some parallel expressions between smooth topological spaces and classical topological spaces. Key Words: Smooth topology, Smooth compactness, Connectedness, Smooth neighbourhood. VI