Generalized form of Continuous Functions by using the concepts of --open sets, --open sets and --open sets.

Abstract

Al-Omeri and Noiri [1] have introduced the notions of -sets, -sets -sets and -sets in an ideal topological spaces. They have also discussed certain properties of these sets and established their relationships. In the present paper, we have defined generalized -I-open and e-I-open sets by considering -open sets derived from the given topological space . We have defined --continuous, --continuous functions and extended this concept of continuity by considering -I- open sets and e-I--open sets to define further generalization. Certain irresolute mappings viz. irresolute, -irresolute, -irresolute, -irresolute and their corresponding homeomorphisms have been also defined. In support of the new definitions relevant illustrative examples have been discussed.