Between Preopen and Open Sets in Topological Spaces: Halgwrd M. Darwesh - Team, Support (Thai Journal of Mathematics, 2013)
The aim of the present paper is to introduce the class of ω_p-open sets which is strictly placed between the class of all preopen and the class of all open subsets of X. Relationships with some other type of sets are given. Furthermore, we introduce a new type of continuity termed the class of ω-almost continuous functions which is lies strictly between the class of all continuous and the class of all almost-continuous functions. New decompositions of continuity are obtained.