Abstract: In this paper, we defined -open set by using s-operation and -closed set, then by using -open set, we define -closed set. In addition we define -closure of subset of ( ) and -interior of subset of by using -closed set and -open set respectively. Furthermore we introduce and discuss minimal -open sets in topological spaces. We establish some basic properties of minimal -open. We obtain an application of a theory of minimal -open sets and define a -locally finite space then we prove, Let be a -locally finite space and a nonempty -open set. Then there exists at least one (finite) minimal -open set such that where is semi-regular.