Semi Regular Weakly Open Sets in Topological Spaces

R. S. Wali; Basayya B Mathad

doi:https://doi.org/10.14445/22315373/IJMTT-V37P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 37 | Number 1 | Year 2016 | Article Id. IJMTT-V37P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V37P506

Semi Regular Weakly Open Sets in Topological Spaces

R. S. Wali, Basayya B Mathad

Abstract

This paper considers a new class of sets called semi-regular weakly open (briefly srw-open) sets are introduced and studied in topological spaces. i.e. A subset G of topological space X is said to be semi-regular weakly open set, if F sin t(A) , whenever F A and F is rwclosed set in X. The new class strictly lies between semi-open sets, rw-open sets and gs-open sets in topological spaces. Also, as applications, using some properties of srw-open sets and srw-closed sets we investigate srw-interior and srw-closure operators and their properties respectively.

Keywords

srw-closed sets, srw-open sets, srwneighbourhoods, srw-interior, srw-closure.

References

[1] S. P. Arya, and T. M. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math.,21(1990), 717–719.
[2] S. S. Benchalli and R. S. Wali, On RW-closed sets in topological spaces, Bull.Malaysian.Math.Sci.Soc. (2) 30(2)(2007), 99-110.
[3] P. Bhattacharyya and B. K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math.29(1987), 376–382.
[4] J. Cao, M. Ganster and I. Reilly, On sg-closed sets and gα- closed sets, mem. Fac. Sci. Kochi Uni. Sera, Math., 20(1999), 1-5.
[5] J. Dontchev, On generalizing semi-preopen sets, Mem. Fac Sci. Kochi. Univ. Ser. A. Math.16(1995,35–48.
[6] S. GeneCrossley and S. K. Hildebrand., Semi-Closure, The Texas Journal of Science, Texas Tech University, Lubbock- 79409, 99-112.
[7] N. Levine, Generalized Closed Sets in Topology, Rend. Cir. Mat. Palermo,2(1970),89-96.
[8] H. Maki, R. Devi and K. Balachandran, 1994.Associated topologies of generalized α-closed sets and α-generalized closed sets, Mem. Sci. Kochi Univ. Ser. A. Math.,15(1994),51–63.
[9] H. Maki, R. Devi and K. Balachandran, Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed.part-III 42(1993),13–21.
[10] A. S. Mashhour, M. E. Abd. El-Monsef and S. N. El-Deeb, On pre continuous mappings and weak pre-continuous mappings, Proc Math, Phys. Soc. Egypt, 53(1982), 47-53.
[11] O. Njastad, On some classes of nearly open sets, Pacific J. Math.,15(1965), 961-970.
[12] N. Palaniappan and Rao, K.C.,Regular generalized closed sets, Kyungpook Math. J. 33(1993), 211–219.
[13] A. Pushpalatha, Studies on Generalizations of Mappings in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore, 2000.
[14] M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math.Soc.,41(1937), 374- 481.
[15] N. V. Velicko, H-closed Topological Spaces, Tran. Amer. Math. Soc., 78(1968), 103-118.
[16] R. S. Wali and Basayya B. Mathad, Semi Regular Weakly closed sets in Topological Space, International Journal of Mathematical Archive-7(6)(2016),91-97.
[17] R. S. Wali and Vijayakumari T Chilakwad, On Pre Generalized Regular Weakly Closed sets in Topological Space, International Journal of Mathematical Archive- 6(1)(2015), 76-85.
[18] R. S. Wali and Prabhavati S. Mendalgeri, On Regular wclosed sets in topological spaces, Int. J. ofMathemaics Archive-5(10)(2014), 68-76.
[19] V. Zaitsav,V., 1968.On certain classes of topological spaces and their bicompactifications.Dokl.Akad.Nauk SSSR 178: 778-779.

Citation :

R. S. Wali, Basayya B Mathad, "Semi Regular Weakly Open Sets in Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 37, no. 1, pp. 36-43, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V37P506