e-Open Sets and Irresolute Functions in Fuzzy Topological Structures

The field of Mathematical Science which goes under the name of topology is concerned with all questions directly or indirectly related to continuity. Fuzzy topologists have introduced and investigated many different generalizations of fuzzy continuous functions. Weaker forms of continuity in fuzzy topology have been developed in the names like fuzzy semi-open sets, fuzzy regular open sets, fuzzy pre-open sets, fuzzy e-open sets, fuzzy b-open sets which have been widely considered by several mathematicians. The results embodied in this thesis are solely concerned with some aspects of fuzzy e-open sets and fuzzy topological structures. In classical topology, Erdal Ekici (2008) has introduced and studied the concepts of e-open set in which a generalization of del-semi open sets and del-preopen sets are introduced. Also, the properties and the relationships of e-open sets are investigated. Further, the concepts of e-continuous function and the decomposition of continuity are studied in elaborately. The concept of fuzzy e-open set is introduced and its properties are studied and the interrelation between the other types of fuzzy open sets is discussed.