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More on Generalizations of Weakly Continuity

M. Lellis Thivagar 1, M. Anbuchelvi 2 & G.Jayaparthasarathy 2
  1. School of Mathematics,Madurai Kamaraj University, Madurai,Tamil Nadu, INDIA1
  2. Department of Mathematics,V.V.Vanniaperumal College for Women,Virudhunagar, INDIA2
  3. Department of Mathematics,St. Jude’s College, Thoothoor,K.K. (Dt) , Tamil Nadu, INDIA2
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International Journal of Innovative Research in Science, Engineering and Technology

Abstract

This paper presents an operator gs ~~ -closure and some of it’s properties are studied.Also two new classes of mappings via gs ~~ -closed sets are introduced and their characterizations are investigated.

Keywords
gs ~~ -closed sets, gs ~~ -closure, gs ~~ -interior, gs ~~ -Frontier. 2010 AMS Subject Classification: 57C05

INTRODUCTION
Many continuous mappings by utilizing different kinds of generalized closed sets were introduced and investigated. Recently, R.Balachandran,P.Sundaram and H.Maki in 1991 [1],defined a new class of generalized continuous mappings. IN 1972,Crosseley and Hildebrand [2] introduced the class of irresolute mappings.In this paper, our objective is to introduce an operator gs ~~ -closure and investigate its properties. Also two new notions such as the classes of mappings gs ~~ -continuity and gs ~~ -irresoluteness are introduced and investigated. Some of their characterizations are studied in terms of gs ~~ -closure.

2 PRELIMINARIES
Throughout this paper, (X, ) (or simply X) represents topological spaces on which no separation axioms are assumed unless otherwise mentioned.For a subset A of X,cl(A),int(A)and c A denote the closure of A,the interior of A and the complement of A respectively. Let us recall the following definitions, which are useful in the sequel.
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3 gs ~~ -CLOSURES
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References
  1. Balachandran, K. ; Sundaram, P. ; Maki, H. : On generalized continuous functions in topological spaces, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 12(1991), 5-13.
  2. Crossley,S.G, and Hildebrand,S.K,"Semi Topological Properties," Fund.Math.,74 (1972),233-254.
  3. Dontchev, J. : Contra-continuous functions and strongly S-closed spaces , Internat. J. Math. & Math.Sci. 19 (1996), 303-310.
  4. Lellis Thivagar,M and Jeya Parthasarathy,G., "A New Sort of Weakly Generalized Closed Sets" (Submitted)
  5. Levine, N. : Semi-open sets and semi-continuity in topological spaces, Amer Math. Monthly, 70(1963), 36-41.
  6. Mashhour, A.S. ; Hasanein, I.A. ; El-Deeb, S.N :  -continuous and  -open functions , Acta Math Hung., 41(3-4)(1983), 213-218.
  7. Sundaram, P. ; Maki, H. ; Balachandran, K. : Semi-generalized continuous maps and Semi- 1/2 T spaces, Bull.Fukuoka Univ.Ed.Part III, 40(1991), 33-40.