Study on some aspects of generalized semi generalized closed sets in classical and fuzzy topological spaces

Abstract

The thesis mainly deals with some aspects of generalized semi generalized closed sets in topological space and fuzzy topological space and applications of fuzzy soft sets in decision making problems newlineIn chapter 1 the preliminaries of the generalized notions of closed and open sets in topological space fuzzy topological space and soft topological space and the brief outline of the thesis are discussed newlineIn chapter 2 a new class of closed and open sets called minimal closed maximal closed minimal open and maximal open sets are introduced Also the new sets namely semi maximal open and semi minimal closed sets are introduced Continuous and irresolute maps via these sets are introduced and some of its properties are established newlineIn chapter 3 the notion of generalized semi generalized closed sets in bitopological space is introduced and its properties are studied The relationship between this newly introduced generalized semi generalized closed set with other existing closed sets in bitopological space is investigated Several characterizations and some interesting properties of this set are given newline newline