On (Rw)*-Open Sets in Topological Spaces

R. S.Wali; Bajirao P Kamble

doi:https://doi.org/10.14445/22315373/IJMTT-V54P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 2 | Year 2018 | Article Id. IJMTT-V54P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P512

On (Rw)*-Open Sets in Topological Spaces

R. S.Wali, Bajirao P Kamble

Abstract

The aim of this paper is to introduce and study the new class of sets called (rw)*-open sets are introduced and studied in topological space i.e. A sub set A of a topological space X is said to be (rw)*-open sets , If U int(cl(A)) ,whenever U A and U is rw-closed sets in X. The new class is properly lies between #rg-open sets and wg-open sets in topological space .Also, as application using properties of (rw)*-open sets and (rw)*-closed stes. We investigate (rw)*-neighbourhoods, (rw)*-derived sets, (rw)*-interior and (rw)*-closure operators and have been discussed some of their basic properties respectively.

Keywords

(rw)*-closed sets, (rw)*-open sets, (rw)*- neighbourhoods, (rw)*-derived sets, (rw)*-interior , (rw)*-closure.

References

[1] N. L evine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(1970), 89-96.
[2] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
[3] M. Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc, 41(1937), 374-481
[4] O. Njastad, on some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970
[5] 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.
[6] M.sheik Join , A study on generalisations of closed seton continuous maps in topological and bitopological spaces ,Ph.D,Thesis Bharthiar University,Coimbatore.(2002).
[7] 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.
[8] J.Tong, weak almost continuous mapping and weakly nearly compact spaces. Boll. Un. Math. Ital. 6, 385-391 (1982).
[9] D. Andrijevic, Semi-preopen sets, Mat. Vesnik . 38(1), 24-32 (1986).
[10] N.V. Velicko, H-closed Topological Spaces, Tran. Amer. Math. Soc., 78 (1968), 103-118.
[11] D.E. Cameron, Properties of s-closed spaces, Prac Amer Math, soc 72,581586 (1978).
[12] J. Dontchev and T. Nori, Quasi-normal space and g-closed sets, Act math. Hungar 89(3) (2000), 21-219.
[13] P. Bhattacharya and B. K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29, 376-382 (1987).
[14] N. Palaniappan and K. C. Rao, Regular generalised closed sets, kyungpook math, J.33 (1993), 211-219.
[15] J. Dontchev, On generalizing semi-preopen sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math.16, 35-48 (1995).
[16] Pushpalatha, Studies on generalizations of mappings in topological spaces, Ph.D. Thesis, Bharathiar University, Coimbatore (2000).
[17] N. Nagaveni, Studies on Generalizations of Homeomorphisms in Topological Spaces, Ph.D. Thesis, Bharathiar University, Coimbatore, 1999.
[18] A.Vadivel & K. Vairamamanickam, rgα-Closed sets& rgα-open sets in Topological Spaces, Int J of Math, Analysis Vol 3, 37,1803-1819 (2009).
[19] 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.
[20] S. Bhattacharya, on generalized regular closed sets, Int J. Contemp. Math science Vol.6, 201,145-152.
[21] C. Janaki & Renu Thomas, on R*- Closed sets in Topological Spaces, Int J of Math Archeme 3(8), 3067-3074 (2012).
[22] S. Mishra, et al. On regular generalized weakly (rgw)-closed sets in topological spaces, Int. J. of Math Analysis Vol 6, no.(30) , 1939-1952 (2012).
[23] Jayalakshmi & C. Janaki, on ωgrα-closed sets in Topological Spaces, Int J of Maths 3(6), 2386-2392 (2012).
[24] M. Anitha & P. Thangavely, On pre generalized pre regular closed sets(pgpr) Acta ciencia Indian, 31M(4) , 1035-10404 (2005).
[25] Shlya Isac Mary & P.Thangavelv, on Regular pre-semi closed sets in topological spaces, KBM J. of Math Sc & Comp Applications (1), 9-17 (2010).
[26] V. Joshi, S.Gupta, N. Bhardwaj, R, Kumar, on Generalised pre Regular weakly(gprω)-closed set in sets in Topological Spaces, Int Math Foruro Vol(7), (40)1981-1992 (2012).
[27] S.Syed Alifathima,M .Mariasingam, #rg-closed set in topological space, Int J of Modern Engineering Research Vol(3).
[28] A.S.Mashhour, I. A. Hasanein and S.N.EI-Deeb, -continuous and -open mapping, Act.math.Hung, 41(1983), 213- 218.
[29] R.S.Wali and P. S. Mandalgeri, on r-open sets in topological spaces. int J. Comp. & Math. Sci. Vol.7 (6), 490-499 (2014)
[30] R.S.Wali and Basayya Mathad. Semi Regular Weakly Open Set in topological spaces int J. Math.Trends & techno (IJMTT)- Vol. 37,2231-5373 (2016)
[31] R.S.Wali and Nirani Laxmi, On RMG-open sets in topological spaces (IOSR-JM) .Vol.12 (4), 46-53 (2016)
[32] R. S. Wali & Bajirao P. Kamble , On (rw)*-closed sets in topological spaces.int J. Comp. & Math. Sci. Vol.7 (4), 192- 202 (2016)
[33] R. S. Wali & vivekanand Dembre, on pgprw-open set and pgpr-neighbourhood in topological spaces. Annal of pure and Applied Mathematics Vol.10, No.1, 2015, 15-20.
[34] R. S. Wali & vivekanand Dembre, on pgprw-closed set in general topological spaces. int J. Comp. & Math. Sci. Vol.6(2), 113-125 (2014).

Citation :

R. S.Wali, Bajirao P Kamble, "On (Rw)*-Open Sets in Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 2, pp. 109-122, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P512