International Journal of Mathematics And its Applications Volume 5, Issue 3–B (2017), 189–198. ISSN: 2347-1557 Available Online: http://ijmaa.in/ A p p l i c a t i o n s • I S S N : 2 3 4 7 - 1 5 5 7 • I n t e r n a t i o n a l J o u r n a l o f M a t h e m a t i c s A n d i t s International Journal of Mathematics And its Applications Connectedness and Compactness via Semi-Star-Regular Open Sets Research Article S.Pious Missier 1* , R.Krishnaveni 2 and G.Mahadevan 3 1 P.G. & Research Department of Mathematics, V.O.Chidambaram College, Thoothukudi, Tamilnadu, India. 2 Department of Mathematics, G.Venkataswamy Naidu College, Kovilpatti, Tamilnadu, India. 3 Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Dindigul, TamilNadu, India. Abstract: In this paper, we introduce new concepts namely, semi*r-connectedness and semi*r-compactness using semi*regular open sets. We investigate their basic properties. We also discuss their relationships with already existing concepts of connect- edness and compactness. MSC: 54D05, 54D30. Keywords: Semi*regular closed, semi*regular closure, semi*regular compact, semi*regular connected, semi*regular open. c  JS Publication. 1. Introduction In 1974, Das [2] defined the concept of semi-connectedness in topological spaces and investigated its properties. Compactness is one of the most important, useful and fundamental concepts in topology. In 1981, Dorsett [5] introduced and studied the concept of semi-compact spaces. Since then, Hanna and Dorsett [6], Ganster [5] investigated the properties of semi-compact spaces. PasunkiliPandian.S [12] introduced semi*-pre-compact spaces and investigated their properties. Robert, A. and Pious Missier, S. recently introduced and studied semi*-connectedness and semi*-compactness [16] in topological spaces. The authors have defined semi*regular open sets [13] and semi*regular closed sets [13] and investigated their properties. In this paper, we introduce the concept of semi*regular connected spaces. We investigate their basic properties. We also discuss their relationship with already existing concepts namely connectedness, semi-connectedness, semi-pre connectedness and semi*α-connectedness. Further we define semi*regular compact spaces and investigate their properties. We also show the relationship of semi*r-compactness with each of the concepts of compactness, semi-compactness semi*-compactness and semi*-pre compactness. 2. Preliminaries Throughout this paper X will always denote a topological space. If A is a subset of the space X, Cl(A) and Int(A) denote the closure and the interior of A respectively. * E-mail: spmissier@gmail.com