On *(gr)-Closed Sets in Topological Spaces

Rajendran.V; Indirani.K; Vijesh.C; Suresh.N

doi:https://doi.org/10.14445/22315373/IJMTT-V24P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 24 | Number 2 | Year 2015 | Article Id. IJMTT-V24P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V24P513

On *(gr)-Closed Sets in Topological Spaces

Rajendran.V, Indirani.K, Vijesh.C, Suresh.N

Abstract

In this paper we introduced and study the notions of *(gr)-closed sets and *(gr)-open sets in topological spaces and also we discussed their properties.

Keywords

*(gr)-closed set, *(gr)-open set, ĝ-open.

References

1. M. E. Abd, El. Monsef, S. N. El. Deeb and R. A. Mashmand, β- open sets and β-Continuous mappings, Bull, Fac. Sci., Assiut Univ., 12(1983), 77- 90.
2. S. P. Arya and T. Naur, Characterizations of S- Normal spaces, Indian J. Pure.Appl.Math., 21(8)(1990), 717- 719.
3. P. Bhattacharya and B. K. Lahiri, Semi- generalized closed sets in topology, Indian J. Math., 29(3)(1987), 375- 382.
4. S. Bhattacharya, On generalized regular closed sets, Int. J. Contemp. Math.Sciences, (6)(2011), 145- 152.
5. J. Dontjev, On generalizing semi- pre open sets, MEM. Fac. Kochi Univ. Ser.A, Math., (16)(1995), 35- 48.
6. Y. Gnanambal, On generalized pre regular closed sets in topological spaces,Indian J. Pure Appl. Math., (28)(1997), 351- 360.
7. N. Levine, Semi- open sets and Semi- continuity in topological spaces, Amer. ath. Monthly., 70(1963), 36- 41.
8. N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo., 19(2)(1970), 89- 96.
9. S. Mashhour, M. E. Abd El. Monsef and S. N. El. Deeb, ON Pre- continuous and weak Pre- continuous mappings, Proc. Math. and Phys. Soc. Egypt, 53(1982), 47- 53.
10. H. Maki, R. Devi and K. Balachandran, Generalized α- closed sets in topology,Bull. Fukuoka Univ. Ed. Part III, 42(1993), 13- 21.
11. H. Maki, J. Uniehara and T. Noiri, Every topological spaces in Pre- T1/2, Mem.Fac. Sci. Kochi Univ. Ser. A, Math., 17(1996), 33- 42.
12. O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961- 970.
13. N. Palaniappan and K. C. Rao, Regular generalized closed sets, Kyungpook Math 33(2)(1993), 211- 219.
14. M. Stone, Applications of the theory of Boolean rings to general topology,Trans. Amer. Math. Soc., 41(1937), 374- 481.
15.M. K. S. Veera Kumar, On ĝ-closed sets in topological spaces, Bull. Allah.Math. Soc. 18(2003), 99-112.

Citation :

Rajendran.V, Indirani.K, Vijesh.C, Suresh.N, "On *(gr)-Closed Sets in Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 24, no. 2, pp. 92-96, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V24P513