Murad \{O}zko\c{c} and G\''ulhan Aslim Ege University Faculty of Science Department of Mathematics, Ege University Faculty of Science Department of Mathematics

Abstract : A new class of generalized open sets in a topological space, called $e\mbox{-}$open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta\mbox{-}$semi-preopen (or $\delta \mbox{-}\beta \mbox{-}$open) sets and weaker than both $\delta \mbox{-}$semiopen sets and $\delta \mbox{-}$preopen sets. In order to investigate some different properties we introduce two strong form of $e\mbox{-}$open sets called $e\mbox{-}$regular sets and $e\mbox{-}\theta \mbox{-}$open sets. By means of $e\mbox{-}\theta \mbox{-}$open sets we also introduce a new class of functions called strongly $\theta \mbox{-}e\mbox{-}$continuous functions which is a generalization of $\theta \mbox{-}$precontinuous functions. Some characterizations concerning strongly $\theta \mbox{-}e\mbox{-}$continuous functions are obtained.