Volume 5 | Number 2 | Year 2014 | Article Id. IJMTT-V5P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V5P514
Andrijivic introduced and studied the concept of b-open sets. Following this Bharathi et.al. introduced the concept of b**-open sets. Recently Indira et.al. studied the notions of *b-open sets and **b-open sets. In this paper, it has been shown that b**-open sets are precisely semi-pre-open sets or -open sets and **b-open sets are nothing but -open sets. Further the notion of a b# -open set is introduced and its basic properties are discussed.
[1] M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, -open sets and -continuous map-pings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77-90.
[2] Ahmad Al-Omari and Mohd.Sahni Md. Noorani, Decomposition of continuity via b-open set, Bol.Soc. Paran. Mat.,(38) v26 1-2 (2008):53-64.
[3] D. Andrijevi c, On b-open sets, Mat. Vesnik 48 (1996), 59-64.
[4] D. Andrijevi c, Semi-preopen sets, ibid. 38 (1986), 24-32.
[5] D.Andrijevi c, Some properties of the topology of -sets, Mat. Vesnik 36 (1984), 1-10.
[6] S. Bharathi, K. Bhuvaneshwari, N. Chandramathi, On locally b**-closed sets, International Journal of Mathematical Sciences and Applications, 1(2) (2011) 636-641.
[7] H.H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math. 8(1964), 351-360.
[8] J.Dontchev and M.Przemski, On the various decompositions of continuous and some weakly continuous functions, Acta Math. Hungar. 71(1-2)(1996), 109-120.
[9] J. Dugundji, Topology, Allyn and Bacon, Boston 1966.
[10] W.Dunham, Weakly Hausdorff spaces, Kyungpook Math.J.,15(1975), 41-50.
[11] L. Gillman, M. Jerison, Rings of continuous functions, Univ. Series in Higher Math., Van Nostrand, Princeton, New York, 1960.
[12] T. Indira and K. Rekha, On locally **b-closed sets, Proceedings of the Heber International Conference on Applications of Mathematics and Statistics (HICAMS) (2012).
[13] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41.
[14] A.S. Mashhour, M.E. Abd El-Monsef and S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47-53.
[15] T.Nieminen, On ultrapseudocompact and related spaces, Ann. Acad. Sci. Fenn., Ser. AI. Math.,3(1977),185-205.
[16] O. Njastad, On some classes of nearly open sets, Paci_c J. Math. 15 (1965), 961-970.
[17] J.H.Park, Strongly -b-continuous functions, Acta Math. Hungar. 110(4)(2006), 347-359.
[18] M.Przemski, A Decomposition of continuous and a-cintinuous, Acta Math. Hungar. 61(1-2)(1993), 93-98.
[19] Thangavelu P, Rao K. C., p–sets in topological spaces, Bull. Pure and Appl. Sci. 21(E)(2)(2002), 341-345.
[20] Thangavelu P, Rao K. C., q–sets in topological spaces, Prog of Maths 36(1&2)(2002), 159-165.
[21] J. Tong, On decomposition of continuity in Topological spaces, Acta Math.Hungar, 54 (1-2) (1989) 51-55.
R.Usha Parameswari , P.Thangavelu, "On b#-Open Sets," International Journal of Mathematics Trends and Technology (IJMTT), vol. 5, no. 2, pp. 202-218, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V5P514