EUROPEAN JOURNAL OF MATHEMATICAL SCIENCES Vol. 1, No. 1, 2012, 27-35 www.ejmathsci.com On Almost γ-continuous Functions Hariwan Z. Ibrahim Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan-Region, Iraq Abstract. We introduce a new class of functions called almost γ-continuous functions which is con- tained in the class of almost continuous functions and contains the class of γ-continuous functions. 2010 Mathematics Subject Classifications: 54A05, 54A10; 54C05 Key Words and Phrases: γ-open, almost γ-continuous 1. Introduction Kasahara [9] defined an operation α on a topological space to introduce α-closed graphs. Following the same technique, Ogata [16] defined an operation γ on a topological space and introduced γ-open sets. Basu et al. [4] introduced a type of continuity called γ-continuous function. Singal and Singal [18] introduced the notion of almost continuity. In this paper, we introduce a new class of functions called almost γ-continuous functions which is contained in the class of almost continuous functions and contains the class of γ- continuous functions. We obtain basic properties of almost γ-continuous functions. 2. Preliminaries Throughout this paper, (X , τ) and (Y, σ) stand for topological spaces with no separation axioms assumed unless otherwise stated. For a subset A of X , the closure of A and the interior of A will be denoted by Cl (A) and Int (A), respectively. Let (X , τ) be a space and A a subset of X . An operation γ [16] on a topology τ is a mapping from τ in to power set P (X ) of X such that V ⊆ γ(V ) for each V ∈ τ, where γ(V ) denotes the value of γ at V . A subset A of X with an operation γ on τ is called γ-open [16] if for each x ∈ A, there exists an open set U such that x ∈ U and γ(U ) ⊆ A. Then, τ γ denotes the set of all γ-open set in X . Clearly τ γ ⊆ τ. Complements of γ-open sets are called γ-closed. The τ γ -interior [10] of A is denoted by τ γ - Int (A) and defined to be the union of all γ-open sets of X contained in A. A topological X with an operation γ on τ is said to be γ-regular [16] if for each Email address: (H. Ibrahim) http://www.ejmathsci.com 27 c  2012 EJMATHSCI All rights reserved.