On S-Precontinuous Multifunctions

Abstract

Abstract. In this paper we introduce and study s-precontinuous multifunctions as a generalization of s-continuous multifunctions and precontinuous multifunctions. Several characterizations and some basic properties of such multifunctions are investigated. IntroductionLet X and Y be topological spaces. A function / : X -> Y is said to be s-continuous In 1988, Popa [13] introduced the notion of precontinuous multifunctions and showed that ii-almost continuity and precontinuity are equivalent for multifunctions.In this paper, we introduce and study s-precontinuous multifunctions as a generalization of s-continuous multifunctions and precontinuous multifunctions. Several characterizations and some basic properties of such multifunctions are investigated. PreliminariesLet X be a topological space and A a subset of X. The closure of A and the interior of A are denoted by CI (A) and Int(A), respectively. A subset A is said to be preopen [8] (resp. semi-open [6},a-open [10]) if A C Int(Cl(j4)) (resp. A C Cl(Int(A)), A C Int(Cl (Int(A)))). The family of all preopen sets of X containing a point a; 6 I is denoted by PO(X, x). The family of all preopen (resp. semi-open) sets in X is denoted by PO(X) (resp. SO(X)).2000 Mathematics Subject Classification: 54C08, 54C60.