journal-of-interdisciplinary-mathematics Journal of Interdisciplinary Mathematics 2169-012X 0972-0502 Taru Publications 10.47974/JIM-2026 Bi-nano topological spaces with grill bi-open sets Jasim Rana H. Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq Yaseen Rana B. Department of Mathematics, College of Education for Women, Tikrit University, Tikrit, Iraq Shihab Ali A. Department of Mathematics, College Education for Pure Sciences, Tikrit University, Tikrit, Iraq 28 3-A 909 915 08 05 2025

The study introduces a new concept in Nano topological spaces is said Grill Bi-Nano topological spaces via studying three issues disjoint of each other rely on the number of equivalence relations for the universe set and its subset and also present definitions for the GN1,2- interior and GN1,2- closure of sets with this framework and we briefly discuss some characteristics of local functions. 

 Grill bi-nano-topological space Grill bi-nano interior Grill bi-nano closure Multi - Granular bi-nano topology new class of Grill bi-nano closed sets access open retracted no