italian journal of pure and applied mathematics – n. 31-2013 (227-238) 227 OPERATION VIA-REGULAR OPEN SETS C. Carpintero Universidad De Oriente Nucleo De Sucre Cumana Venezuela e-mail: carpintero.carlos@gmail.com N. Rajesh Department of Mathematics Rajah Serfoji Govt. College Thanjavur-613005 Tamilnadu India e-mail: nrajesh topology@yahoo.co.in E. Rosas Universidad De Oriente Nucleo De Sucre Cumana Venezuela e-mail: ennisrafael@gmail.com Abstract. The aim of this paper is to introduce and study the concepts of γ -regular open sets and their related notions in topological spaces. Keywords: γ -open set, γ -regular open set, γ -δ-open set. 2000 Mathematics Subject Classification: 54D10. 1. Introduction Generalized open sets play a very important role in General Topology and they are now the research topics of many topologists worldwide. Indeed a significant theme in General Topology and Real analysis concerns the various modified forms of continuity, separation axioms etc. by utilizing generalized open sets. Kasahara [3] defined the concept of an operation on topological spaces and introduce the concept of γ -closed graphs of a function. Ogata [6] introduced the notion γ -open