Generalized Quotient Functions in Topological Spaces

Abstract

Levine [2] offered a new and useful notion in General Topology, that is the notion of a generalized closed. A subset A of a topological space (X, ?)is called generalized closed (briefly g-closed) if cl(A) ? U whenever A ? U and U is open in (X,?). This notion has been studied extensively in recent years by many topologists. The investigation of generalized closed sets had led to several new and interesting concepts. After the introduction of generalized closed there are many research papers which deal with different types of generalized closed. Recently Ravi and Ganesan [6] have introduced g¨-closed and studied their properties using sg-open set [1]. In this chapter we introduce g¨-quotient maps. Using these new types of maps, several characterizations and its properties have been obtained. Also the relationship between strong and weak forms of g¨-quotient maps have been established.