International Journal of Mathematical Archive-6(6), 2015, 182-186 Available online through www.ijma.info ISSN 2229 – 5046 International Journal of Mathematical Archive- 6(6), June – 2015 182 ON NANO GENERALISED CONTINUOUS FUNCTION IN NANO TOPOLOGICAL SPACE K. BHUVANESWARI 1 , K. MYTHILI GNANAPRIYA* 2 1 Professor and Head, Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, Tamilnadu, India. 2 Research Scholar, Department of Mathematics, Karpagam University, Coimbatore, Tamilnadu, India. (Received On: 04-06-15; Revised & Accepted On: 25-06-15) ABSTRACT The purpose of this paper is to introduce a new class of continuous functions called Nano generalized continuous functions and to discuss some of its properties in terms of Ng –closed sets, Nano g-closure and Nano g- Interior. Keywords: Nano Topology, Ng-closed sets, Nano g-closure, Nano g-interior, Nano g- continuous Function, Nano g-closed map, Nano g- Homeomorphism. I. INTRODUCTION Continuous functions is one of the main concepts of Topology. In 1991, Balachandran [1] et.al, introduced and studied the notions of generalized continuous functions. Different types of generalizations of continuous functions were studied by various author in the recent development of Topology. The notion of Nano topology was introduced by Lellis Thivagar [3] which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it and also defined Nano closed sets, Nano-interior and Nano-closure. He has also defined Nano continuous functions, Nano open mapping, Nano closed mapping and Nano Homeomorphism. In [2] Bhuvaneswari et.al, introduced and studied some properties of Nano generalized closed sets in Nano topological spaces. In this paper we have introduced a new class of continuous functions called Nano generalized continuous functions and discuss some of its properties in terms of Ng –closed sets, Nano g-closure and Nano g- Interior. II. PRELIMINARIES Definition: 2.1[5] A subset A of (X, τ) is called a generalized closed set (briefly g-closed) if cl(A) ⊆ U whenever A ⊆ U and U is open in X. Definition: 2.2 [1] A map f: (X, τ) → (Y, σ) is called g- continuous if  −1 () is g- open in (X,τ) for every open set V in (Y, σ ) Definition:2.3 [3 ]Let U be a non-empty finite set of objects called the universe and R be an equivalence relation on U named as indiscernibility relation. Then U is divided into disjoint equivalence classes. Elements belonging to the same equivalence class are said to be indiscernible with one another. The pair (U, R) is said to be the approximation space. Let X ⊆ U. Then, (i) The lower approximation of X with respect to R is the set of all objects which can be for certain classified as X with respect to R and is denoted by L R (X). L R (X)=U{R(x):R(x) ⊆ X, xєU} where R(x) denotes the equivalence class determined by xєU. (ii) The upper approximation of X with respect to R is the set of all objects which can be possibly classified as X with respect to R and is denoted by U R (X). U R (X) = U{R(x): R(x) ∩X≠Ф, xєU} (iii) The boundary region of X with respect to R is the set of all objects which can be classified neither as X nor as not – X with respect to R and it is denoted by B R (X). B R (X) = U R (X) - L R (X). Corresponding Author: K. Mythili Gnanapriya* 2 2 Research Scholar, Department of Mathematics, Karpagam University, Coimbatore, Tamilnadu, India.