IHJPAS. 36(2)2023 306 This work is licensed under a Creative Commons Attribution 4.0 International License. Abstract The objective of this paper is to define and introduce a new type of nano semi-open set which called nano   -open set as a strong form of nano semi-open set which is related to nano closed sets in nano topological spaces. In this paper, we find all forms of the family of nano   -open sets in term of upper and lower approximations of sets and we can easily find nano   -open sets and they are a gate to more study. Several types of nano open sets are known, so we study relationship between the nano   -open sets with the other known types of nano open sets in nano topological spaces. The Operators such as nano   -interior and nano   -closure are the part of this paper. Keywords: nano closed sets, nano semi-open sets, nano   -open sets, nano   -interior, nano   - closure. 1.Introduction The notion of nano topological space (briefly ) introduced by Thivagar and Carmel [1] with respect to a subset  of a universe  which is defined in terms of lower and upper approximations. Levine [2] introduced the notions of semi-open. Later, nano semi-open sets introduced by Thivagar Carmel [1], also nano   -open sets introduced by [4], and more nano open sets defined in [5-7]. In this paper, we introduce the concept nano   -open sets as a strong form of nano semi-open sets, since every nano   -open (briefly   -oprn) sets is nano semi-open sets and the relationship with some class of nano near open sets. All forms of family of nano   -open sets under various cases of approximations idea also derived. Also, operators such as nano   -interior and nano   -closure are the part of this paper. doi.org/10.30526/36.2.2958 Article history: Received 14 August 2022, Accepted 12 September 2022, Published in April 2023. Ibn Al-Haitham Journal for Pure and Applied Sciences Journal homepage: jih.uobaghdad.edu.iq Nano   -Open Sets In Nano Topological Spaces Nehmat K. Ahmed Department of Mathematics, College of Education, Salahaddin University-Erbil, 44001, Erbil. nehmat.ahmed@su.edu.krd Osama T. Pirbal Department of Mathematics, College of Education, Salahaddin University-Erbil, 44001, Erbil. osama.pirbal@su.edu.krd