International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) | IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss.8| Aug. 2014 | 1| Contra  * Continuous Functions in Topological Spaces S. Pious Missier 1 , P. Anbarasi Rodrigo 2 I. Introduction Dontchev[3] introduced the notion of contra continuity. Later Jafari and Noiri introduced and investigated the concept of contra  continuous and discussed its properties. Recently, S.Pious Missier and P. Anbarasi Rodrigo [9] have introduced the concept of  * -open sets and studied their properties. In this paper we introduce and investigate the contra  * continuous functions and almost contra  * continuous functions and discuss some of its properties. II. Preliminaries Throughout this paper (X, IJ), (Y, ı ) and (Z,  ) or X , Y , Z represent non-empty topological spaces on which no separation axioms are assumed unless otherwise mentioned. For a subset A of a space (X, IJ), cl(A) and int(A) denote the closure and the interior of A respectively. The power set of X is denoted by P(X). Definition 2.1: A subset A of a topological space X is said to be a  *open [9] if A  int* ( cl ( int* ( A ))). Definition 2.2: A function f: (X, IJ) ⟶ (Y, ı ) is called a  * continuous [10] if f -1 (O) is a  *open set of (X, IJ) for every open set O of (Y, ı ). Definition 2.3: A map f: (X, IJ) ⟶ (Y, ı ) is said to be perfectly  * continuous [11] if the inverse image of every  *open set in (Y, ı ) is both open and closed in (X, IJ) . Definition 2.4: A function f: (X, IJ) ⟶(Y, ı) is said to be  *Irresolute [10] if f -1 (O) is a  *open in (X, IJ) for every  *open set O in (Y, ı ). Definition 2.5: A function f: (X, IJ) ⟶ (Y, ı ) is called a contra g continuous [2] if f -1 (O) is a g - closed set [6] of (X, IJ) for every open set O of (Y, ı ). Definition 2.6: A function f: (X, IJ) ⟶ (Y, ı ) is called a contra continuous [3]if f -1 (O) is a closed set of (X, IJ) for every open set O of (Y, ı ). Definition 2.7: A function f: (X, IJ) ⟶ (Y, ı) is called a contra  continuous [5] if f -1 (O) is a  closed set of (X, IJ) for every open set O of (Y, ı ). Definition 2.8: A function f: (X, IJ) ⟶ (Y, ı) is called a contra semi continuous [4] if f -1 (O) is a semi closed set of (X, IJ) for every open set O of (Y, ı ). Definition 2.9: A function f: (X, IJ) ⟶ (Y, ı) is called a contra g  continuous [1] if f -1 (O) is a g  -closed set of (X, IJ) for every open set O of (Y, ı ). Definition 2.10: A Topological space X is said to be  *T 1/2 space or  *space [9] if every  * open set of X is open in X. Definition 2.11: A Topological space X is said to be a locally indiscrete [7] if each open subset of X is closed in X. Definition 2.12: Let A be a subset of a topological space (X, IJ ). Th e set ∩{U ∈ IJ | A ⊂ U} is called the Kernel of A [7] and is denoted by ker(A). Lemma 2.13: [6] The following properties hold for subsets A,B of a space X: 1. x ∈ ker(A) if and only if A ∩ F   ,for any F ∈ C(X, x); Abstract: In [3], Dontchev introduced and investigated a new notion of continuity called contra- continuity. Recently, Jafari and Noiri [5] introduced new generalization of contra-continuity called contra  continuity . The aim of this paper is to introduce and study the concept of a contra  * continuous and almost contra  * continuous functions are introduced MATHEMATICS SUBJECT CLASSIFICATIONS: 54AO5 Keywords And Phrases: contra  * continuous functions, almost contra  * continuous functions, contra  * graph , and locally  * indiscrete space.