EURASIAN BULLETIN OF MATHEMATICS EBM (2018), VOL. 1, NO. 3, 85-93 On Some New Notions in Nano Ideal Topological Spaces M. Parimala 1 , S. Jafari 2, * Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam-638401, Tamil Nadu, India 1 College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark. 2 Abstract. The purpose of this paper is to introduce the notion of nano ideal topological spaces and investigate the relation between nano topological space and nano ideal topological space. Moreover, we offer some new open and closed sets in the context of nano ideal topological spaces and present some of their basic properties and characterizations. 2010 Mathematics Subject Classifications: 54A05; 54A10; 54B05 Key Words and Phrases: Nano ideals, nano local functions, topological ideals, nano toplogical ideals 1. Introduction An ideal [6] I on a nonempty set X is a nonempty collection of subsets of X which satisfies (i) A ∈ I and B ⊂ A implies B ∈ I and (ii) A ∈ I and B ∈ I implies A ∪ B ∈ I . Given a topological space (X, τ ) with an ideal I on X and if P (X) is the set of all subsets of X, a set operator (.) * : P (X) → P (X), called a local function [5] of A with respect to τ and I is defined as follows: for A ⊂ X, A * (I,τ )= {x ∈ X : U ∩ A/ ∈ I for every U ∈ τ (x)}, where τ (x)= {U ∈ τ : x ∈ U }. A Kuratowski closure operator cl * (.) for a topology τ * (I,τ ), called the *-topology, finer than τ is defined by cl * (A)= A ∪ A * (I,τ ) [11]. When there is no chance for confusion, we will simply write A * for A * (I,τ ) and τ * for τ * (I,τ ). If I is an ideal on X, then the space (X,τ,I ) is called an ideal space. A subset A of an ideal space is said to be *-dense in itself [3] (resp. τ * -closed [5]) if A ⊂ A * (resp. A * ⊂ A). By a space (X, τ ), we always mean a topological space (X, τ ) with no separation properties assumed. If A ⊂ X, then cl(A) and int(A), denote the closure and interior of A in (X, τ ), respectively. The interior of A in (X, τ * ) is denoted by int * (A). The notion of I -open sets was introduced by Jankovic et al. [5], and further it was investigated by T.R. Hamlett et al [2] and Abd El-Monsef et al.[1]. The notion of a nano ideal topological space was introduced by Parimala et al. [10]. They studied its properties and characterizations. In this paper, we introduce some new notions in the context of nano ideal topological spaces and investigate their basic properties. * Corresponding author. Email address: jafaripersia@gmail.com * (Corresponding Author) http://www.ibujournals.com 85 c  2018 EBM All rights reserved.