Some Variants of Normality in Relative Topological Spaces

Abstract

With each topological property $\mathcal{P}$ one can associate a relative version of it formulated in terms of location of $Y$ in $\emph{X}$ in such a natural way that when $Y$ coincides with $X$ then this relative property coincides with $\mathcal{P}$. Arhangel'skii and Ganedi introduced this concept of relative topological properties in 1989. The concept of mild normality or $\kappa$-normality was introduced independently by Singal and Singal in 1973 and Stchepin in 1972. A few years earlier in 1969, Singal and Arya studied the concept of almost normality. V. Zaitsev in 1968 introduced the concept of quasi normal spaces while $\pi$-normality was studied by Lutfi. N. Kalantan in 2008. In this paper we have studied these variants of normality in relative sense.