Topological Studies On Hdeibs Closed Sets and#61559; Via Idealization

Abstract

In the first chapter, we discuss some the objectives of this Ph. D work. and#61549;In the second Chapter, we introduce the notions Tg and#61549;-spaces, gTg -spaces, and#61549;Tg -spaces and obtain their properties and characterizations. In the third Chapter, we introduce a new class of sets, namely s-closed, in topologicaland#61537;g spaces and study their basic properties. In the fourth chapter, we introduce g -quotient maps. Using these new types of maps,and#61537; several characterizations and its properties have been obtained. Also the relationship between strong and weak forms of g -quotient maps have been established.and#61537; In the fifth chapter, we introduce a new class of sets namely (1,2)* -g and#61549; -closed in (1,2)-closed and the class of (1,2)*and#61556;bitopological spaces. This class lies between the class of (1,2)-closed and the class of (1,2)*and#61556;-gclosed. This class also lies between the class of -closed.and#61559;- In the sixth chapter, we obtain decompositions of (1,2)* -g and#61549; -continuity in bitopological spaces using (1,2)* - p g -continuity, (1,2)* - g -continuity, (1,2)* - t g -continuity and (1, 2)* - * g -continuity. In the seventh chapter, we introduce (1,2)* -g and#61549; -closed functions, (1,2)* -g and#61549; -open functions, (1,2)* -g *-closed functions and (1,2)*and#61549; -g *-open functions in bitopological spacesand#61549; and obtain certain characterizations of these classes of functions. Also we introduce (1,2)* -g *and#61549; - homeomorphisms and study their properties. In the eigth chapter, we introduce three forms of (1, 2) * -locally closed called (1,2) * -and#61549;-g locally closed, (1,2)* -lc*and#61549;-g and (1,2)* -lc** sets. Properties of these new concepts are studiedand#61549;-g as well as their relations to the other classes of (1,2)* -locally closed will be investigated. newline