Set strongly 1-starcompact and set $\mathcal{K}$-starcompact spaces

Abstract

In this paper, we consider new types of set star covering properties called set strongly 1-starcompact and set $\mathcal{K}$-starcompact. We investigate the relationship between these two properties and some other set covering properties. We study the topological properties of introduced classes of spaces. Further we give  the partial solutions of two open problems posed by Singh in \cite{singh2021set}.