Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47887120210101On $Smathcal{I}H$-property and $SSmathcal{I}H$-property in topological spaces657612305010.22034/kjm.2020.209741.1637ENManojBhardwajUniversity of Delhi, IndiaBrij KishoreTyagiA.R.S.D. College, University of Delhi, IndiaSumitSinghUniversity of Delhi, IndiaJournal Article20191129In 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.http://www.kjm-math.org/article_123050_1b4fd9d46b351f7934667d2db3661eb8.pdf