A study of tri topological spaces

Abstract

Having motivated by the introduction of semi open set in a topological space by N.Levine in the year 1963, many Mathematicians started the work of similar generali-zations.Also the new generalizations were extended to bitopological spaces. In this thesis we concentrate on extending the generalizations to tri topological spaces. we introduce tri topological space and we study tri and#61537; open set,tri and#61537; closed set,tri and#61537; interior of a set, tri and#61537; closure of a set and similar concepts using and#61538; open sets. We introduce many generalized topologies from a tri topological space. Also we discuss the common properties of the generalization of tri topological space. With the idea of extending the limit concept to tri topological space we have defined and studied generalized filters. We have introduced two new kuratowski closure operators by introducing the concepts net closed sets and filter closed sets . Some results are extended to fuzzy tri topological space and generalized tri topological space. With the interest of generating more tri topological spaces, we have introduced and#61556;1and#61556;2and#61556;3 open sets, and#61556;123 open sets . The various directions of research work in topology namely generalizations of open sets, finding new topologies from old and extending fuzzy concepts to topological spaces are combined here and hence this research work has a wide scope for further extensions in different directions.