A Study On Ω-closed Sets, Ω_s-closed Sets And Strong (θ,s)-continuous Functions

There are three chapters in this paper. In the first chapter, we introduce necessary preliminaries and main results of this paper.In the second chapter, we studyΩ-closed sets andΩ_s-closed sets. Properties ofΩ-closed sets andΩ_s-closed sets are investigated in this chapter. We obtain some decomposition theorems and characterizations of extremely disconnected spaces byΩ-closed sets andΩ_s-closed sets. We also give the idealization of the decomposition theorems.In the third chapter, we introduce the notions of strong (θ, s)-continuous functions. We investigate some properties of strong (θ, s)-continuous functions. Some characterizations of strong (θ, s)-continuous functions are obtained. Some characterizations of extremely disconnected spaces and hyperconnected spaces are also obtained by strong (θ, s)-continuous functions.