Continuity and Separation Axioms Based on βc-Open Sets

Abstract

In this thesis, we study a new class of sets called βc-open sets which is contained in the class of β-open sets and contains the class of bc-open sets. We prove that the topology generated by the family of βc-open sets in a natural way is the same as the topology of θ-open sets in extremally disconnected Alexandroff spaces. Moreover, we introduce βccontinuous functions as a new class of continuous functions and give a characterization of these functions. Finally, we define βc-g.closed sets and investigate new separation axioms βc-Tk, k ∈ {0;½; 1; 2}.