1451 13 archive 33 disk0/00/00/14/51 2007-12-17 05:06:54 2008-08-16 01:41:53 2007-12-17 05:06:54 article show Benchalli, S.S. benchalli_math@yahoo.com Wali, R.S. rswali@rediffmail.com Karnatak University, Dept. of Mathematics pub Q none Regular semiopen sets, rw-closed sets. In this paper, a new class of sets called regular w-closed (briefly rw-closed) sets in topological spaces is introduced and studied. A subset $A$ of a topological space $(X,\tau )$ is called rw-closed if $U$ contains closure of $A$ whenever $U$ contains $A$ and $U$ is regular semiopen in $(X,\tau )$. This new class of sets lies between the class of all w-closed sets and the class of all regular g-closed sets. Some of their properties are investigated. 2000 Mathematics Subject Classification: 54A05 2007 published Bulletin of the Malaysian Mathematical Sciences Society 30 2 Penerbit Universiti Sains Malaysia 99-110 TRUE 0126-6705 http://math.usm.my/bulletin/pdf/v30n2/v30n2p2.pdf http://math.usm.my/bulletin/html/vol30_2_2.htm [1] M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12(1983), 77—90. [2] D. Andrijevic, Semi-preopen sets, Mat. Vesnik 38(1986), 24—32. [3] S.P. Arya and T.M. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math. 21(1990), 717—719. [4] P. Bhattacharyya and B.K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math. 29(1987), 376-382. [5] N. Biswas, On characterization of semi-continuous functions, Atti Accad. Nez. Lincei Rend, CL Sci. Fis. Mat. Natur. 48(8)(1970), 399—402. [6] D.E. Cameron, Properties of S-closed spaces, Proc. Amer Math. Soc. 72(1978), 581—586. [7] S.G. Crossley and S.K. Hildebrand, Semi-closure, Texas J. Sci. 22(1971), 99-112. [8] G. Di Maio and T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math. 18(3)(1987), 226-233. [9] J. Dontchev, On generalizing semi-preopen sets, Mem. Fac Sci. Kochi. Univ. Ser. A. Math. 16(1995), 35—48. [10] J. Dontchev and M. Ganster, On δ-generalized set T¾ spaces, Mem. Fac. Sci. Kochi Uni. Ser. A. Math. 17(1996), 15—31. [11] J. Dontchev and T. Noiri, Quasi-normal spaces and πg-closed sets, Acta Math. Hungar. 89(3)(2000), 211—219. [12] J. Dontchev and H. Maki, On θ-generalized closed sets, Topology Atlass, www.Unipissing.ca/topology/p/a/b/a/08.htm. [13] J. Dontchev and H. Maki, On sg-closed sets and semi-λ closed sets, Questions and Answers Can. Topology 15(1997), 253—266. [14] G.L. Garg and D. Sivaraj, On sc-compact and S-closed spaces, Boll. Un. Mat. Ital. 6(3B)(1984), 321-332. [15] Y. Gnanambal, On generalized preregular closed sets in topological spaces, Indian J. Pure App. Math. 28(1997), 351—360. [16] Y. Gnanambal and K. Balachandran, On gpr-continuous functions in topological spaces, Indian J. Pure Appl. Math. 30(6)(1999), 581—593. [17] D.S. Jankovic and I.L. Reilly, On semi separation properties, Indian J. Pure Appl. Math. 16(1985), 957—964. [18] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36—41. [19] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Pelermo 19(1970), 89—96. [20] H. Maki, J. Umehara and T. Noiri, Every topological space is pre-T½, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. 17(1996), 33—42. [21] H. Maki, R. Devi and K, Balachandran, Associated topologies of generalized α-closed sets and α-generalized closed sets, Mem. Sci. Kochi Univ. Ser. A. Math. 15(1994), 51-63. [22] H. Maki, R. Devi and K. Balachandran, Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. part-III 42(1993), 13—21. [23] A.S. Mashhour, I.A. Hasanein and S.N. El-Deeb, α-open mappings, Acta. Math. Hungar. 41(1983), 213—218. [24] A.S. Mashhour, M.E. Abd. El-Monsef and S.N. El-Deeb, On pre continuous mappings and weak pre-contiouous mappings, Proc Math, Phys. Soc. Egypt 53(1982), 47—53. [25] N. Nagaveni, Studies on Generalizations of Homeomorphisms in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore, 1999. [26] T.Noiri, On almost open mappings, Memoir Miyakonojo Tech. College 7(1972). [27] 0. Njastad, On some classes of nearly open sets, Pacific J. Math. 15(1965), 961—970. [28] N. Palaniappan and K.C. Rao, Regular generalized closed sets, Kyungpook Math. J. 33(1993), 211—219. [29] J.K. Park and J.H. Park, Mildly generalized closed sets, almost normal and mildly normal spaces, Chaos, Solutions and Fractals 20(2004), 1103—1111. [30] A. Pushpalatha, Studies on Generalizations of Mappings in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore, 2000. [31] P. Sundaram and M. Sheik John, On w-closed sets in topology, Acta Ciencia Indica 4(2000), 389-392. [32] M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41(1937), 374—481. [33] J. Tong, Weak almost continuous mapping and weak nearly compact spaces, Boll. Un. Mat. Ital. 6(1982), 385-391. [34] M.K.R.S. Veera Kumar, Between closed sets and g-closed sets, Mem. Fac. Sci. Kochi Univ. (Math.) 21(2000), 1—19. [35] N.V. Velicko, H-closed topological spaces, Trans. Amer. Math. Soc. 78(1968), 103—118.