Some variants of normality in relative topological spaces

Abstract

With each topological property P one can associate a relative version of it formulated in terms of the location of Y in X in such a natural way that when Y coincides with X, then this relative property coincides with P. Arhangel?skii and Genedi introduced this concept of relative topological properties in 1989. The concept of mild normality or ?-normality was introduced independently by Singal and Singal in 1973 and Scepin in 1972. A few years earlier in 1969, Singal and Arya studied the concept of almost normality. V. Za?cev in 1968 introduced the concept of quasi normal spaces while ?-normality was studied by Kalantan in 2008. In this paper we study these variants of normality in a relative sense.