On strongly star ideal compactness of topological spaces

In this article we introduce the concept of strongly star $\mathrm{I}$-compactness and study some of its topological features. We represent some finite intersection like properties for both I-compact spaces and strongly star $\mathrm{I}$-compact spaces. Lastly we establish a relation between the countably $I_{fin}$-compact space and the strongly star $I_{fin}$-compact space. In order to identify the difference between the different versions of compactness we represent some counter examples. And some open problems are also posed in this article.