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