JMAT_V5_N2_A1 g*b-Homeomorphisms S.Bharathi Journal on Mathematics 2277-5137 5 2 1 5 g-Closed Homeomorphisms, g*-Closed Homeomorphisms, g*b-Closed Homeomorphisms The aim of this paper is to define and develop a new type of homeomorphism called g*b-homeomorphism. Some of their properties and several characterizations of these types of functions with others are discussed in this paper. Some of the implications, relationships and independence relationships with few of the existing closed sets are studied and also, the author investigates the relationship between these classes of functions. April - June 2016 Copyright © 2016 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=6003