Abstract
The concept of nano topological spaces induced by different neighborhoods was originally proposed by Thivagar and Priyalatha. The endeavor of the current work is to propose a certain extension of the previous concept called I-nano topological spaces induced by different neighborhood. This concept based on ideals. Some important characteristics and significant properties of these spaces are presented. We provide a comparative study of the present spaces and the previous one. It turn out that every nano topological space induced by different neighborhoods is an I-nano topological space induced by different neighborhoods. Afterwards, to emphasize these results some counter examples are considered. An application from the real life problems is presented. Eventually, the notions of j-ideal generalized nano closed sets and its properties are studied.