R*- Closed Maps and R*- Open Maps in Topological Spaces

Janaki. C; Renu Thomas

Volume : II, Issue : VI, June - 2013

R- Closed Maps and R- Open Maps in Topological Spaces

Janaki. C, Renu Thomas

Abstract :

This paper introduces the idea of R*–interior and R*–closure in addition to the concept of R*–open and R*–closed maps. Certain properties of R*–open and R*–closed are also discussed. 1. SUMMARY The generalization of closed sets was introduced by N.Levine[7]. This contribution led to many new concepts and results in general topology .Researchers like Arya et al [2] Balachandran et al [3] Arokiarani et al [1] Palaniappan et al [10] have worked on different types of generalized closed sets .Closed mapping in topology was introduced by Malghan [9].Similar studies on wg–closed maps and rwg–closed maps were studied by Nagaveni [8,11] M.Karpagadevi [5], A.Vadivel [12,13],Antony Rex Rodrigo [6]defined RW–closed maps ,rgα–closed maps and R–closed maps respectively. In this paper, the notion of R*–interior and R*–closure have been defined and their basic properties are studied. For any subset A of X, the complement of R*–interior of A is R*–closure.In addition , this paper includes a new class of closed maps called R*–closed maps. Its relation with similar closed maps is discussed and some properties related to this map are obtained. Throughout the paper, X and Y denote the topological spaces (X, ) and (Y, ) respectively on which no separation axioms are assumed