arXiv:1103.3770v1 [math.GN] 19 Mar 2011 γ ∗ -semi-open Sets in Topological Spaces-II Bashir Ahmad * and Sabir Hussain ** * Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan. Present Address: Department of Mathematics, King Abdul Aziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. E. mail: drbashir9@gmail.com ** Department of Mathematics, Islamia University Bahawalpur, Pakistan. Present Address: Department of Mathematics, Yanbu University, P. O. Box 31387, Yanbu, Saudi Arabia. E. mail: sabiriub@yahoo.com Abstract. In this paper, we continue studying the properties of γ * -semi-open sets in topologi- cal spaces introduced by S. Hussain, B. Ahmad and T. Noiri[8]. We also introduce and discuss the γ * -semi-continuous functions which generalize semi-continuous functions defined by N. Levine [10]. Keywords. γ -closed (open) sets, γ -closure , γ * -semi-closed (open) sets, γ * -semi-closure, γ -regular, γ * -semi-interior, γ -semi-continuous functions, γ -semi-open (closed) mappings. AMS(2000)Subject Classification. Primary 54A05, 54A10, 54D10. 1 Introduction A. Csaszar [6,7] defined generalized open sets in generalized topological spaces. In 1975, Maheshwari and Prasad [11] introduced concepts of semi-T 1 -spaces and semi-R 0 -spaces. In 1979, S. Kasahara [9] defined an operation α on topological spaces. In 1992 (1993), B. Ahmad and F.U. Rehman [1, 13] introduced the notions of γ -interior, γ -boundary and γ -exterior points in topological spaces. They also studied properties and characterizations of (γ ,β )-continuous mappings introduced by H. Ogata 1