On $Smathcal{I}H$-property and $SSmathcal{I}H$-property in topological spaces

Abstract

In this paper, we further investigated the $SS mathcal{I} H$ and $S mathcal{I} H$ properties introduced by Das et. al recently. It is shown that regular-closed $G_delta$ subspace of $SS mathcal{I} H$ (resp., $S mathcal{I} H$) is not $SS mathcal{I} H$ (resp., $S mathcal{I} H$). The preservation properties of these spaces are studied under some maps. Also $SS mathcal{I} H$ and $S mathcal{I} H$ properties are investigated in Alexandroff space.