On a Class of γ*-pre-open Sets in Topological Spaces

Abstract

Abstract. In this paper, a new class of open sets, namely -pre-open sets was intro-duced and its basic properties were studied. Moreover a new type of topology ˝ p wasgenerated using -pre-open sets and characterized the resultant topological space (X,˝ p ) as -pre-T 12 space. 1. IntroductionThe concepts of pre-open sets and semi-pre-open sets were introduced respec-tively by Mashhour et al.[6] and Andrijevic[1]. Andrijevic[1] introduced a new classof topology generated by pre-open sets and corresponding closure and interior op-erators. Kasahara[3] de ned the concept of an operation on topological spaces andintroduced the concept of -closed graphs of an operation. Ogata[7] called the op-eration (respectively -closed set) as -operation (respectively -closed set) andintroduced the notion of ˝ which is the collection of -open sets in a topologicalspace. Further, he de ned the concept of -closure and ˝-closure operators and * Corresponding Author.Received April 6, 2011; accepted September 11, 2012.2010 Mathematics Subject Classi cation: 54A05, 54A10, 54D10.Key words and phrases: -closed(open), -closure, -interior, -pre-closed(open), -pre-closure, -pre-interior, -semi-pre-closed(open), -semi-pre-closure, -semi-pre-interior, ˝-p-closed(open), ˝-p-closure, ˝-p-interior.