On Quasi-Normal and Quasi-Regular Spaces in Hereditary Generalized Topological Spaces

M. Vigneshwaran, K. Baby

Abstract: The concept of generalized open sets in generalized topologies was investigated by Csaszar. In this paper we introduce spaces namely Quasi - -regular spaces, Almost - -Normal spaces and Quasi ultra - -Normal spaces with a fixed set of parameters and obtain some properties in the light of these notion. We also introduce Quasi - -regular spaces and Quasi - -normal spaces and investigate some properties of these new notions by using some basic properties of (,) -continuity in generalized topological spaces introduced by M. Rajamani, V. Inthumathi and R. Ramesh. Moreover we obtain relations between Quasi - normal spaces and Almost - -normal spaces with respect to (,) -continuity and (,) -open map.

Keywords: Quasi - -normal spaces, Quasi - -regular spaces, Quasi ultra - -Normal space, Almost - -Normal spaces, , -continuity and, -open, , -irresolute, , -continuous, , R-irresolute, , R-pre-closed