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.
The third author extend her appreciation to the Deanship of
Scientific Research at King Khalid University for funding this work through research
groups program under grant (R.G.P.1/148/40).
"Generalization of nano topological spaces induced by different neighborhoods based on ideals and its applications." Tbilisi Math. J. 14 (1) 135 - 148, March 2021. https://doi.org/10.32513/tmj/19322008111