Y – Continuity and Y – Connectedness in Topological Space

Abstract

In 2011 A.I. EL Maghrabi and A.M. Mubaraki introduced and studied the notions of Y – open and Y – closed sets in general topology as well as presented some characterizations of these notions. We introduce and investigate several properties and characterizations of a new class of maps between topological spaces called Y – open maps, Y – closed maps, Y – continuous maps and Y – irresolute maps. We also introduce slightly Y – continuous, totally Y – continuous and almost Y – continuous maps between topological spaces and establish several characterizations of these new forms of maps. Furthermore, we introduce and study the notions of Y – separated sets and Y – connectedness in topological spaces.