WEAK FORMS OF ??OPEN SETS

In general topology, many authors introduced and studied some classes of weak or strongforms of open sets in topological spaces. In 1970 Levine, [6], introduced the notion of a generalized open sets which is weak form of open sets. In 1982 Hdeib [4] introduced the notionof a ??open sets which is weak form of open sets. In 1983 the authors [1] introduced theweak form for an open set which is called a ??open set. In 2005 Al-Zoubi [2] introduced thegeneralization property of ??open sets to get the weak form of ??open sets. In 2009 Noiriand Noorani [7] introduced the notion of ???open set which is weak form for a ??open setsand a ??open sets.This paper is organized as follows. Section 2 is devoted to some preliminaries. In Section 3we introduce the concept of generalized ???open sets by utilizing the ???closure operator.Furthermore, the relationship with the other known sets will be studied. In Section 4 weintroduce the notions of ???continuous, generalized ???continuous, Slightly and Contra???Continuous functions.