~ 31 ~ ISSN Print: 2394-7500 ISSN Online: 2394-5869 Impact Factor: 5.2 IJAR 2017; 3(6): 31-38 www.allresearchjournal.com Received: 08-04-2017 Accepted: 09-05-2017 RS Wali Department of Mathematics, Bhandari and Rathi College, Guledagudda, Karnataka, India Vijayalaxmi R Patil Department of Mathematics, Rani Channamma University Belagavi, Karnataka, India Correspondence RS Wali Department of Mathematics, Bhandari and Rathi College, Guledagudda, Karnataka, India On rgwα -Closed and rgwα -Open maps in topological spaces RS Wali and Vijayalaxmi R Patil Abstract The aim of this paper is to introduce new type of closed maps rgw⍺-closed maps and rgw⍺-open maps, rgw⍺*-closed maps and rgw⍺*-open maps. We also obtain some properties of rgw⍺-closed maps and rgw⍺-open maps. Keywords: rgw⍺-closed maps, rgw⍺*-closed maps and rgw⍺-open maps, rgw⍺*-open maps Mathematical subject classification (2010): 54C10 1. Introduction Mappings play an important role in the study of modern mathematics, especially in Topology and Functional Analysis. Closed and open mappings are one such mapping which are studied for different types of closed sets by various mathematicians for the past many years. Generalized closed mappings were introduced and studied by Malghan [17] . wg-closed maps and rwg-closed maps were introduced and studied by Nagavani [21] . Regular closed maps, gpr-closed maps, rg-closed maps and rg⍺-closed and rg⍺-open maps have been introduced and studied by Long [24] , Gnanambal [12] , Arockiarani [13] , A.Vaidivel and K.Vairamanickam [34] respectively. In this paper, a new class of maps called regular generalized weakly ⍺- closed (briefly, rgw⍺-closed) maps, rgw⍺*- closed maps have been introduced and studied their relations with various generalized closed maps. Also we defined rgw⍺-open maps and rgw⍺*-open maps and studied some of its properties. Let us recall the following definitions which are used in our present study. 2. Preliminaries Throughout this paper, (X, τ) and (Y, σ) (or simply X and Y) represent a topological spaces on which no separation axioms are assumed unless otherwise mentioned. For a subset A of a space X, cl(A) and int(A) denote the closure of A and the interior of A respectively. X\A or A c denotes the complement of A in X. Definition 2.1: A subset A of a topological space (X, τ) is called 1. Semi-open set [23] if A ⊆ cl(int(A)) and semi-closed set if int(cl(A)) ⊆ A. 2. Pre-open set [18] if A ⊆ int(cl(A)) and pre-closed set if cl(int(A)) ⊆ A. 3. α-open set [14] if A ⊆ int(cl(int(A))) and α -closed set if cl(int(cl(A)))⊆ A. 4. Semi-pre open set [1] (=β-open) if A ⊆ cl(int(cl(A)))) and a semi-pre closed set (=β- closed) if int(cl(int(A))) ⊆ A. 5. Regular open set [32] if A = int(clA)) and a regular closed set if A = cl(int(A)). 6. Regular semi open set [10] if there is a regular open set U such that U ⊆ A ⊆ cl(U). 7. Regular α-open set [34] (briefly, rα-open) if there is a regular open set U s.t U ⊆ A ⊆ αcl (U). Definition 2.2: A subset A of a topological space (X, τ) is called 1. W-closed set [31] if cl(A) ⊆ U whenever A⊆ U and U is semi-open in X. 2. Wα- closed set [8] if αcl(A) ⊆ U whenever A⊆ U and U is w-open in X. 3. Generalized closed set(briefly g-closed) [22] if cl(A) ⊆ U whenever A ⊆ U and U is open in X. International Journal of Applied Research 2017; 3(6): 31-38