%0 Journal Article %T On $S\mathcal{I}H$-property and $SS\mathcal{I}H$-property in topological spaces %J Khayyam Journal of Mathematics %I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures) %Z 2423-4788 %A Bhardwaj, Manoj %A Tyagi, Brij Kishore %A Singh, Sumit %D 2021 %\ 01/01/2021 %V 7 %N 1 %P 65-76 %! On $S\mathcal{I}H$-property and $SS\mathcal{I}H$-property in topological spaces %K Hurewicz space %K Stone-$acute{C}$ech compactification %K strongly star-$mathcal{I}$-Hurewicz %K star-$mathcal{I}$-Hurewicz property %R 10.22034/kjm.2020.209741.1637 %X 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. %U https://www.kjm-math.org/article_123050_1b4fd9d46b351f7934667d2db3661eb8.pdf