The idea of the present study is based on the fundamental idea of defining a new set, which we called interior isolated set and the old topological concept of isolated point. Therefore, the topological properties of this concept and its most important relationships were examined. Moreover, we built new types of sets and spaces as follows: IIS*-set, IIS-open and TIIS-space. The most important algebraic properties of these sets were also studied. In addition, several new definitions were presented for compact based on interior isolated set, which was called IIS-compact spaces IIS-O-compact. The researcher also discussed their most important properties and relationships with each other.