On α-strongly θ-continuity, αθ-openness and (α, θ)-closed graphs in Topological Spaces

Chae et. al. (1995) have studied the concept of a-strongly q-continuous functions and (a, q)-closed graph. The aim of this paper is to investigate several new characterizations and properties of a-strongly q-continuous functions and (a, q)-closed graph. Also, we define a new type of functions called aq-open functions, which is stronger than quasi a-open and hence strongly a-open, and we obtain some characterizations and properties for it. It is shown that the graph of f, G ( f ) is (a, q)-closed graph if and only if for each filter base Y in X q-converging to some p in X such that f (Y) a-converges to some q in Y holds, f ( p) = q.