IOSR Journal of Mathematics (IOSRJM) ISSN: 2278-5728 Volume 2, Issue 4 (Sep-Oct 2012), PP 09-15 www.iosrjournals.org www.iosrjournals.org 9 | Page Note on Intuitionistic N-Closed Sets 1 M. Lellis Thivagar & 2 M. Anbuchelvi 1 School Of Mathematics Madurai Kamaraj University, Madurai-625021.Tamil Nadu, INDIA . 2 Department of Mathematics, V.V.Vanniaperumal College For Women,Virudhunar-626001. Tamil Nadu, INDIA. Abstract: In this paper we introduce and investigate intuitionistic N -closed sets and Intuitionistic almost regular space in a intuitionistic topological spaces. Key words and Phrases: ฀ int ( A), ฀ cl (A), intuitionistic almost regular spaces,intuitionistic N -closed sets., AMS subject classification 2010 :57D05. I. Introduction First, D.Coker et al [2] introduced intuitionistic fuzzy topological spaces, intuitionistic topological spaces and the concept of Compactness on Intuitionistic topological spaces.In this paper we introduce and investigate intuitionistic Almost regular spaces and intuitionistic N-closed sets on intuitionistic topological spaces.Also we investigate their properties via intutionistic ) ( 2 i T -spaces. II. Preliminaries Throughout this paper ) ~ , ~ (  X (or briefly X ~ ) represent intuitionistic topological space on which no separation axioms are assumed unless explicitly stated. Let us recall the following definitions, which are useful in the sequel. Definition II.1. [1] Let X be a nonempty set.An intuitionistic set A is an object of the form ) , ( = 2 1 A A A where 1 A and 2 A are disjoint subsets of X . The set 1 A is the set of all members of A and 2 A is the set of all non-members of A . Definition II.2. [1] Let X be a nonempty set, X a  and ) , ( = 2 1 A A A be an intuitionistic subset of . X Intuitionistic set ) } { }, ({ = ~ c a a a is called an intuitionistic point in . X The intuitionistic point A a  ~ iff 1 A a  . Definition II.3. [1] Let X be a nonempty set. ) , ( = 2 1 A A A , ) , ( = 2 1 B B B and } )/ , ( = { (2) (1) I i A A A i i i  are intuitionistic subsets of . X Then (i) B A  iff 1 1 B A  and . 2 2 A B  (ii) B A = iff B A  and . A B  (iii) ). , ( = 1 2 A A A c (iv) ). , ( = (2) (1) i i i A A A    (v) ). , ( = (2) (1) i i i A A A    (vi) ) , ( = ~ X   . (vii) ). , ( = ~  X X Definition II.4. [2] An intuitionistic topology on a nonempty set X is a family  ~ of intuitionistic sets in X containing ฀ Φ , X ~ and closed under finite infima and arbitrary suprema. Then the pair ) ~ , ~ (  X is called an intuitionistic topological space.Every member of  ~ is known as an intuitionistic open set in X ~ The complement c A of an intuitionistic open set A is called intuitionistic closed set in X ~ . Definition II.5. [2] Let X be a nonempty set and let A be an intuitionistic subset of X. Then the intuitionistic