Further study of ideal topological spaces

Abstract

The thesis consists of seven chapters, the details of which are given newlinebelow. A general introduction, definition of the problem, methodology and newlineobjectives of the research work are presented in the First Chapter. newlineIn the Second Chapter, we define the new notion called gand#948;-closed sets newlinein ideal topological spaces. Also we define the new space called and#948;-*-normal newlinespaces. Properties of such new sets and spaces are obtained on the line of newlineresearch.In the Third Chapter, we define and study the new space called quasip- newlinenormal spaces. Further some new functions of topological spaces are newlineintroduced and studied in detail. Some preservation theorems are given. newlineIn the Fourth Chapter, the concept of and#969;-closed sets was introduced in newlinethe field of topological spaces. It is proved that the family of all and#969;-closed subsets newlineof any set will form a topology. Generalization of and#969;-closed sets has been studied newlinein detail. Some important theorems are obtained. Examples and counter newlineexamples are given to substantiate the concept in the thesis. newlineIn the Fifth Chapter, three new forms of locally closed sets are newlinedefined and studied. Also some new topological and ideal topological subsets newlineare defined and introduced in and#61559;and#61472;-topological spaces. Some decompositions of newline*-continuity are given.In the Sixth Chapter, some new weak structures are introduced and newlinestudied. Properties and characterizations of such new structures are investigated newlinein detail. Some examples using infinite sets are used to s newline newline