International Journal of Research in Advent Technology, Vol.7, No.3, March 2019 E-ISSN: 2321-9637 Available online at www.ijrat.org 1253 New Class of Generalized Closed Sets in Supra Topological Spaces G.Jayaparthasarathy 1 , V. Little Flower 2, M.Arockia Dasan 3 1,2,3 Department of Mathematics, St. Jude’s College Thoothoor-629 176, Kanyakumari, Tamil Nadu (INDIA). Manonmaniam Sundaranar University, Tirunelveli Email: jparthasarathy123@gmail.com 1 , vlflower1998@gmail.com 2 , dassfredy@gmail.com 3 Abstract- In this paper we introduce supra -closed sets and we show that the class of supra -closed sets lies between the class of supra α-closed sets and the class of supra generalized semi-closed sets. We also introduce and discuss some properties of -spaces, -spaces, -spaces. Further we define and investigate the properties of supra- -continuous functions. Index Terms- Supra α-closed sets, Supra gs-closed sets, Supra -closed sets, Supra- -continuous function. 1. INTRODUCTION Extensive research on generalizing closedness was done in recent years by many Mathematicians. In 1983, A.S.Mashhour et al.[17] introduced the concept of supra topological spaces. M.Caldas et al.[5] introduced and studied supra α- open sets and its continuity. In 2010, O.R.Sayed [20] concentrated on supra pre-open sets and supra pre- continuity on topological spaces. In 1970, Levine.N [13] introduced and established the properties of generalized closed sets in classical topology. Many researchers [ 1, 2, 4, 6, 18] turned their attention to define new sets and functions in topological spaces. In 1980, Levine and Dunham [7] further characterized some more properties of generalized closed sets. Noiri et al. [15] proved that every topological space is pre- -space. Further some spaces are derived by Maheshwari and Prasad [16]. Recently Jayaparthasarathy, Hydar Akca and Jamal Benbourenane [8, 9] defined and investigated some properties of the new class of generalized closed sets namely -closed sets. In this paper we define and discuss a new class of weakly α- generalized closed set in supra topological spaces called supra -closed set and investigate its properties. We observe that the class of supra -closed sets lies between the class of supra α-closed sets and the class of supra generalized semi-closed sets. By applying supra -closed sets, we introduce and establish some properties of - spaces, -spaces. Moreover the supra - continuous functions are defined and its properties are investigated. 2. PRELIMINARIES In this section we recall some basic definitions and properties of supra topology which are useful in sequel. Definition 2.1 Let X be a non-empty set. A sub collection μ of P(X) where P(X) denote the power set of X, is said to be a supra topology on X [17] if (i) , X ∈ μ (ii) μ is closed under arbitrary union. The pair (X, μ) is called supra topological space. The element of μ are called the supra open sets in (X, μ) and the complement of the supra open sets are called supra closed sets. Definition 2.2 Let (X, μ) be a supra topological space and A ⊆ X .Then (i) The supra closure of A is denoted by (A)[17], defined as (A)=∩ {B : B is supra closed set and A ⊆ B}. (ii) The supra interior of A is denoted by (A) [17], defined as (A)=∪ {B : B is supra open set and A ⊇ B}. Definition 2.3 Let (X, τ) be a topological space and µ be a supra topology on X. We call μ is a supra topology associated with τ [17] if τ ⊆ μ. Definition 2.4 Let (X , ) be a supra topological space. A subset A of X is called i) supra -open [14] if ⊆ ))). ii) supra semi-open [12] if ⊆ )). iii) supra pre-open [3] if ⊆ )). The complement of a supra α-open set (resp. supra semi-open, and supra pre-open) is called supra α- closed (resp. supra semi-closed, and supra pre-closed). Theorem 2.5 (i) Every supra open set (supra closed set) is supra α-open set (supra α-closed set) [5]. (ii) Let (X, τ) be a topological space and µ be a supra topology associated with τ . Then a subset A of X is supra α-open (supra α-closed) set if and only if it is supra semi-open (supra semi -closed) set and supra pre-open (supra pre-closed) set [5, 20]. Definition 2.6 A subset A of a supra topological space (X, μ) is called