On slightly /spl alpha/-continuous functions

L Introduction Since the concept of feeble continuity has been introduced in [6] , the weak and strong forms of it have been studied by topologists. In 1982, Chae [lo] defined the notion of an almost feeble continuity and studied its properties and relations between them. In this note, spaces X, Y and 2 mean topological spaces on whch no separation axioms are assumed. Let S c X. The closure and interior of S will be denoted by Cl(S) and Int(S), respectively. S is said to be semi-open [SI if there exists an open set 0 such that 0 c S c Cl(0) and its complement is called semiclosed. The intersection of all semi-closed sets containing S is called the semi-closure of S and it will be denoted by sCl(S). S is said to be a-open [3] if S c Int(Cl(Int(S))) and its complement is called a-closed. The intersection of all a-closed sets containing S is called the a-closure of S and it will be denoted by aCl(S). S is said to be feebly open [ 101 if there exists an open set 0 such that 0 c S c sCl(0). From now on, we will denote the family of all a-open (resp. semi-open, open and clopen) sets of X by aO(X) (resp. SO(X), z(X) and CO(X)), and denote the family of a-dpen (resp. semi-open, open and clopen) sets containing x by aO(X, x) (resp. SO(X, x), z(X, x) and CO(X, x)).