On generalized star ωαI-closed sets in ideal topological spaces ∗

V Pankaja; S Gowri

doi:10.48165/

Authors

V Pankaja Department of Mathematics, Sri G.V.G. Visalakshi College for Women (Autonomous), Palani Road, Udumalpet, Tamil Nadu-642128, India.
S Gowri . Research Scholar, Department of Mathematics, Sri G.V.G. Visalakshi College for Women (Autonomous), Palani Road, Udumalpet, Tamil Nadu-642128, India.

DOI:

https://doi.org/10.48165/

Keywords:

ω-closed sets, ωαI-closed sets, ωαI-open sets

Abstract

In this paper, we introduce a new class of sets named as generalized star ωαI-closed sets in ideal topological spaces and study some of their properties. Further we also define and study the concept of ωαI-open sets in ideal topological spaces and discuss their properties.

References

Carpintero, C., Rosas, E., Salas, M., Sanabria, J. and Vasquez, L. (2013) Generalization of ω-closed sets via operators and ideals, Sarajevo Journal of Mathematics, 9(22), 293–301. [2] Dontchev, J. (1996). On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2. [3] Ekici, Erdal (2012). On prefiI-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces, Acta Universitatis Apulensis, 30, 293–303.

Hatir, E. and Noiri, T. (2002). On decomposition of continuity via idealization, Acta Math. Hun gar., 96(4), 341–349.

Jafari, S., Benchalli, S.S., Patil, P.G. and Rayanagoudar, T.D. (2012). Pre g∗-closed sets in topo logical spaces, Journal of Advanced Studies in Topology, 3(3), 55–59.

Jankovic, D. and Hamlett, T.R. (1990). New topologies from old via ideals, Amer. Math. Monthly, 97(4), 295–310.

Kuratowski, K. (1996). Topology, Vol.I, Academic Press, New York.

Maragathavalli, S. and Vinodhini, D. (2014). On α generalized closed sets in ideal topological spaces, IOSR Journal of Mathematics, 10(2), 33–38.

Navaneethakrishnan, M. and Joseph, J. Paulraj (2008). G-closed sets in ideal topological spaces, Acta Mathematica Hungarica, 119(4), 365–371.

Ravi, O., Kamaraj, M. and Vijeyrani, V.Ba. (2016). g#-closed sets in ideal topological spaces, International Journal of Mathematics and its Applications, 4(2), 73–83.

Ravi, O., Tharmar, S., Rodrigo, J. Antony Rex and Sangeetha, M. (2011). Between ∗-closed sets and I∗gficlosed sets in ideal topological spaces, International Journal of Advances In Pure and Applied Mathematics, 1(2), 38–51.

Sundaram, P. and John, M. Shrik (2000). On ω-closed sets in topology, Acta Ciencia Indica, 26(4), 389–392.

Vaidyanathaswamy, R. (1945). The localization theory in set Topology, Proc. Indian Acad. Sci. Math. Sci., 20, 51–61.

Veerakumar, M.K.R.S. (2003). g ̂-closed sets in topological spaces, Allahabad Math. Soc., 18, 99–112.

Veerakumar, M.K.R.S. (2003). g#-closed sets in topological spaces, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 24, 1–13.