# On $S\mathcal{I}H$-property and $SS\mathcal{I}H$-property in topological spaces

Document Type : Original Article

Authors

1 University of Delhi, India

2 A.R.S.D. College, University of Delhi, India

10.22034/kjm.2020.209741.1637

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.

Keywords