Journal of Advanced Studies in Topology ISSN: 2090-388X online Vol. 2, No. 2, 2011, 7–15 c  2011 Modern Science Publishers www.m-sciences.com RESEARCH ARTICLE On Λ λ -Closed Sets in Topological Spaces M. Gilbert Rani ∗ , S. Pious Missier † and S. Jafari ‡ ∗† Postgraduate and Research Department of Mathematics, V. O. Chidambaram College, Tuticorin-628 001, Tamilnadu, India. ‡ Department of Mathematics and Physics, Roskilde University, Postbox 260, 4000 Roskilde-Denmark. (Received: 4 February 2011, Accepted: 11 April 2011) This paper deals with the notions of Λ λ * -set and Λ λ -closed sets which are defined by utilizing the notion of λ-open and λ-closed sets. Keywords: Λ-set; λ-open sets; λ-closed sets; Λ λ * -set; Λ λ -closed sets; Λ λ -open sets. AMS Subject Classification: 54B05, 54C08, 54D05. 1. Introduction In 1997, Arenas [1] introduced the notions of λ-closed sets and λ-open sets in topological spaces. In 1986, Maki [2] introduced the concept of Λ-sets in topological spaces as the sets that coincide with their kernel. In this paper,we define and study some new sets and spaces by using the notion of λ-closed sets and λ-open sets. In section 3, We introduce and investigate the notion of Λ λ * -set. By definition, a subset A of a space (X, τ ) is called a Λ λ * -set if A is the intersection of all λ-open sets containing A. It turns out that the family τ Λ λ * of Λ λ * -set of a space (X, τ ) is a topology for X . In section 4, We introduce and investigate Λ λ -closed set. The definition as follows: A subset A of a topological space (X, τ ) is called Λ λ -closed if A = L ∩ C where L is a Λ λ * -set and C is a λ-closed set. We also investigate some results related to the separation axioms λT 1 , λT 1 2 , λT 0 , λR 0 , λT 1 4 in section 5. 2. Preliminaries Throughout this paper, (X, τ ) denote topological space in which no separation axioms are assumed unless explicitly stated. We recall the following: Definition 2.1 [3] A subset A of the topological space (X, τ ) is said to be a λ-closed set if A = L ∩ F where L is a Λ-set and F is a closed set in X . A subset A is said to be λ-open if its complement is λ-closed. Theorem 2.2 A topological space (X, τ ) is called Alexandroff if every point has a minimal neighbor- hood, or equivalently, has a unique minimal base. * Corresponding Author Email: gilbertrani.rani@gmail.com