On #𝛼-Regular Generalized Closed In
Topological Spaces

S.Thilaga Leelavathi; M.Mariasingam

doi:https://doi.org/10.14445/22315373/IJMTT-V56P571

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 8 | Year 2018 | Article Id. IJMTT-V56P571 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P571

On #𝛼-Regular Generalized Closed In Topological Spaces

S.Thilaga Leelavathi, M.Mariasingam

Abstract

In this paper we introduce a new class of sets called #α- regular generalized closed (briefly , #αrg-closed ) sets in topological space. We prove that this class lies between #rg-closed sets and αg-closed sets. We discuss some basic properties of # regular generalized closed sets.

Keywords

rw-open sets,#rg-closed sets, #αrg-closed sets

References

[1] Benchalli, S.S., and Wali. R.S., on RW-Closed sets in topological spaces, Bull, Malays, Math.Sci.Soc(2) 30(2)(2007), 99-110.
[2] Bhattacharyya. P. And Lahiri. B.K. Semi-generalized closed sets in topology, Indian J. Math 29(1987), 376-382.
[3] Buswas, N., On Characterization of semi-continuous functions, Atti Accad, Naz. Lincei Rend,Cl.Sci.Fis.Mat. Natur. 48(8) (1970), 399-402.
[4] Cameron, D.E., Properties of S-closed spaces, Proc.Amer Math.Soc.72(1978), 581-586.
[5] Dontchev. J and Noiri. T Quasi-normal spaces and πg-closed sets, Acta Math. Hungar, 89(3)(2000), 211-219.
[6] Gnanmbal Y., On generalized pre-regular closed sets in topological spaces, Indian J. Pure App. Math. 28 (1997), 351-360.
[7] Gnanambal. Y. And Balachandran. K., On gpr-continuous functions in topological spaces, Indian J. Pure Appl. Math. 30(6)(1999), 581-593.
[8] Levine. N., Semi-open sets and semi-continuity in topological spaces, Amer, Math. Monthly, 70(1973), 36-
[9] Levine. N., Generalized closed sets in topology, Rend Circ. Mat. Palermo 19(1970), 89-96.
[10] Maki. H. Devi. R and Balachandran, K., Associated topologies of generalized α-cloed and α- generalized closed sets, Mem.Sci.Kochi Univ. Ser. A. Math 15(1994), 51-63.
[11] Mashhour. A.S., ABD. El-Monsef. M.e. and El-Deeb S.N., On pre continuous mappings and weak pre- continuous mappings, Proc Math, Phys. Soc. Egypt 53(1982), 47-53.
[12] Nagaveni. N., Studies on Generalizations of Homeomorphisms in Topological Spaces., Ph.D. Thesis, Bharathiar University, Coimbatore, 1999.
[13] Palaniappan N., and Rao. K.c., Regular generalized closed sets, Kyungpook Math. J. 33(1993),211-219.
[14] Palaniappan N, Pious Missier S and Antony Rex Rodrigo αgp -closed sets in Topological Spaces , Acta Ciencia Indica Vol.XXXI M, No.1,243 (2006).
[15] Park. J.K. and Park, J.H., Mildly generalized closed sets, almost normal and mildly normal spaces, Chaos Solitions and Fractals 20(2004), 1103-1111.
[16] Pushpalatha. A., Studies on Generalizations of Mappings in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore, 2000.
[17] Sundaram. P and Shiek John. M., On w-closed sets in topology, Acta Ciencia Indica 4(2000), 389-392.
[18] Stone. M., Application of the theory of Boolean rings to general topology, Trans. Amer .Math. Soc.41(1937), 374-481.
[19] Syed Ali Fathima S and Mariasingam M on #regular generalized closed sets in Topological Spaces, International Journal of Mathematical Archive -2(11),2011 2497-2502.
[20] Tong.J., Weak almost continuous mapping and weak nearly compact spaces, Boll. Un.Mat.Ital. (1982),385-391.
[21] Thakur C.K. Raman, Vidyottamma Kumari and Sharma M.K α--Generalized & α * - Separation Axioma for Topological Spaces, IOSR Journal of Mathematics Volume 10, Issue 3 Ver.VI(May-Jun 2014) PP 32-36.

Citation :

S.Thilaga Leelavathi, M.Mariasingam, "On #𝛼-Regular Generalized Closed In Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 8, pp. 551-556, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P571