Journal of Advanced Research in Pure Mathematics Vol. 1, No. 1, 2009, pp. 1-9 Online ISSN: 1943-2380 Some properties of s ∗ g - locally closed sets K. Chandrasekhara Rao 1, * and K. Kannan 2 Department of Mathematics, SASTRA University, Srinivasa Ramanujan Centre, Kumbakonam, India. Abstract. In this paper we continue the study of s * g - locally closed sets and s * g - submaximal spaces in general topology. In particular it is proved that s * g - locally closed sets are closed under finite intersections. Also some implications of s * g - locally closed sets are given and we establish that some implications are not reversible, which are justified with suitable examples. Further some distinct notions of s * glc - continuity are introduced and we discuss some of their consequences like the composition of two s * glc - continuous functions and the restriction maps of s * glc - continuity. Keywords: s * g - locally closed sets, s * glc - continuous, s * glc - irresolute, s * g - submaximal space. 2000 Mathematics Subject Classifications: 54A05 1 Introduction In recent years generalization of closed sets plays an important role in developing sep- aration axioms in topological spaces. Also some other new properties are defined by variations of the property of submaximality with the help of dense subsets and locally closed sets. K. Chandrasekhara Rao and K. Joseph [4] introduced the concepts of semi star generalized open sets { named omega - open set in [30] and g ∧ - open in [31]}and semi star generalized closed sets { named omega - closed set in [30] and g ∧ - closed in [31]} in topological spaces. The difference of two closed subsets of an n-dimensional Euclidean space was con- sidered by Kuratowski and Sierpinski [13] in 1921 and the implicit in their work is the notion of a locally closed subset of a topological space (X, τ ). Following Bourbaki [3], Ganster and Reilly [8] introduced locally closed sets in topological spaces and studied three different notions of generalized continuity, namely, lc - continuity, lc - irresolteness * Correspondence to: K. Chandrasekhara Rao, Department of Mathematics, SASTRA University, Srini- vasa Ramanujan Centre, Kumbakonam, 612 001 India. Email: k.chandrasekhara@rediffmail.com 1 and anbukkannan@rediffmail.com 2 † Received: 21 October 2008, Revised: 27 December 2008, Accepted: 11 January 2009. http://www.i-asr.org/jarpm.html 1 c 2009 Institute of Adnanced Scientific Research