Applications of operations on generalized topological spaces

Abstract

In this paper γ_µ -open sets and γ_µ -closed sets in a GTS ( X,µ ) have been studied, where γ_µ is an operation from µ to P( X ). In general, collection of γ_µ -open sets is smaller than the collection of µ -open sets. The condition under which both are same are also established here. Some properties of such sets have been discussed. Some closure like operators are also defined and their properties are discussed. The relation between similar types of closure operators on the GTS ( X,µ ) has been established. The condition under which the newly defined closure like operator is a Kuratowski closure operator is given. We have also defined a generalized type of closed sets termed as γ_µ -generalized closed set with the help of this newly defined closure operator and discussed some basic properties of such sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have shown some preservation theorems of such generalized concepts.