Journal of Advanced Studies in Topology eISSN: 2090-388X pISSN: 2090-8288 Vol. 4, No. 1, 2013, 48–54 c ⃝ 2013 Modern Science Publishers www.m-sciences.com RESEARCH ARTICLE πgp-Normal Topological Spaces L. N. Thanh Nhon ∗ and B. Quang Thinh TGU University, 119 Ap Bac, My Tho, Tien Giang, Viet Nam. (Received: 30 June 2012, Accepted: 22 September 2012) The main aim of this paper is to introduce and study a new stronger version of p-normality called πgp-normality. We prove that πgp-normality is a topological property and it is a hereditary property with respect to π-open πgp-closed subspaces. Keywords: Regular closed; π-closed; p-closed; πgp-closed; p-normal; g * -pre-normal; strongly normal; (p, πgp) - R 0 space. AMS Subject Classification: 54D15, 54D10, 54C08, 54C10. 1. Introduction In 2009, S. S. Benchalli, T. D. Rayanagoudar and P. G. Patil have introduced the notion of g * -Pre normal space by using the notion of g * p-closed sets and studied some properties of it. In this paper, by using πgp-closed, πgp-open sets and π-open sets, we will introduce a new class of spaces called πgp-normal space. We present some characterizations and preservation theorems of this property. We show that this axiom is a hereditary property with respect to πgp-closed, π-open subspaces. Some basic properties are given. 2. Preliminaries Throughout this paper, (X, T) and (Y, O) represent non empty topological spaces on which no separe- tion axioms are assumed, unless explicitly stated and they are simply written X and Y respectively. For a set A of space X , X \A, A, int (A) denote to the complement, the closure and interior of A in X , respectively. Next, we need to recall the following definitions. Definition 2.1 [1] A subset A of a space X is said to be regular open or an open domain if it is the interior of its own closure, or equivalently if it is the interior of some closed set. A set A is said to be regular closed or closed domain if its complement is an open domain. Definition 2.2 [2] A subset A of a space X is called a π-open if it is a finite union of open domain subsets of X . A subset A is called a π-closed if its complement is a π-open. Definition 2.3 [3] A subset A of a space X is said to be pre-open (breifly p-open) if A ⊆ int ( A ) . The complement of p-open set is called p-closed. The intersection of all p-closed sets containing A is called p-closure of A and denoted by pcl (A). Dually, the p-interior of A denoted by pint (A), is defined to * Corresponding author Email: nonh.maths@gmail.com