creators_name: Caldas, M., creators_name: Jafari S., creators_name: Saraf, R.K., creators_id: gmamccs@vm.uff.br creators_id: jafari@stofanet.dk creators_id: type: article datestamp: 2007-12-17 05:06:53 lastmod: 2008-08-16 01:58:04 metadata_visibility: show corp_creators: Universidade Federal Fluminense, Dept. de Matematica Aplicada corp_creators: College of Vestsjaelland South corp_creators: Govt. K.N.G. College, Dept. of Mathematics title: On Some Maps Concerning gα-Open Sets ispublished: pub subjects: Q full_text_status: none keywords: Topological spaces, gα-closed sets, α-open sets, α-open maps, α-irresolute maps, α-T½ spaces. abstract: In this paper, we consider a new generalization of $\alpha$-open maps via the concept of g$\alpha$-closed sets which we call approximately $\alpha$-open maps. We study some of its fundamental properties. It turns out that we can use this notion to obtain a new characterization of $\alpha-T_\frac{1}{2}$ spaces. 2001 Mathematics Subject Classification: 54805, 54C08 date: 2007 date_type: published publication: Bulletin of the Malaysian Mathematical Sciences Society volume: 30 number: 2 publisher: Penerbit Universiti Sains Malaysia pagerange: 93-98 refereed: TRUE issn: 0126-6705 official_url: http://math.usm.my/bulletin/pdf/v30n2/v30n2p1.pdf related_url_url: http://math.usm.my/bulletin/html/vol30_2_1.htm referencetext: [1] D. Andrijevic, Some properties of the topology of α-sets, Mat. Vesnik 36(1984), 1-10. [2] P. Bhattacharyya and P.K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math. 29(1987), 376-382. [3] N. Biswas, On characterization of semi-continuous functions, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Mat. Natur. 48(1970), 399-402. [4] Caldas, M. and J. Dontchev, On spaces with hereditarily compact α-topologies, Acta Math. Hungar. 82(1999), 121—129. [5] Caldas, M. and G. Navalagi, On weakly α-open functions between topological spaces, Internat. J. Math. Sci. 3(2004), 39-51. [6] Caldas, M. and Jafari S., On some low separation axioms in topological spaces, Houston J. of Math. 29(2003), 93—104. [7] Caldas, M., D.N. Georgiou and Jafari S., Characterization of low separation axioms via α-open sets and α-closure operator, Bol. Soc. Paran. Mat. 21(2003), 97-111. [8] Caldas, M. and C. Baker, Contra pre semiopen maps, Kyungpook Math. J. 40(2000), 379-389. [9] R. Devi, K. Balachandran and H. Maki, Generalized α-closed maps and α-generalized closed maps, Indian J. Pure Appl. Math. 29(1998), 37—49. [10] J. Dontchev, On some separation axioms associated with the α-topology, Mem. Fac. Sci. Kochi Univ. (Math.) 18(1997), 31—35. [11] J. Dontchev, On point generated spaces, Q & A in General Topology 13(1995), 63-69. [12] Jafari S. and T. Noiri, Some remarks on weakly α-continuity, Far East J. Math. Sci. 6(1998), 619-625. [13] S.N. Maheshwari and S.S. Thakur, On α-irresolute mappings, Tankang J. Math. 11(1980), 209-214. [14] A.S. Mashhour, I.A. Hasanein and S.N. EL-Deeb, α-continuous and α-open mappings, Acta Math. Hungar. 41(1983), 213—218. [15] H. Maki, R. Devi and K. Balachandran, Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. 42(part III)(1993), 13—21. [16] 0. Njastad, On some classes of nearly open sets, Pacific J. Math. 15(1965), 961—970. [17] T. Noiri, Weakly α-continuous function, Internet. J. Math. Math. Sci. 10(1987), 483-490. [18] P. Sundaram, H. Maki and K. Balachandran, Semi-generalized continuous maps and Semi-T½ spaces, Bull. Fukuoka Univ. Ed. 40(Part, III)(1991), 33—40. citation: Caldas, M., and Jafari S., and Saraf, R.K., (2007) On Some Maps Concerning gα-Open Sets. Bulletin of the Malaysian Mathematical Sciences Society, 30 (2). pp. 93-98. ISSN 0126-6705