πJ*-Closed Sets in Topological Spaces

Hamant Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V68I2P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 2 | Year 2022 | Article Id. IJMTT-V68I2P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I2P503

πJ*-Closed Sets in Topological Spaces

Hamant Kumar

Abstract

In this paper, a new class of sets called πJ*-closed sets is introduced and its properties are studied. The relationships among closed, r-closed, r*-closed, δ-closed, πJ*-closed and other generalized closed sets are investigated. Several examples are provided to illustrate the characterizations of these new classes of sets.

Keywords

η*-closed, r*-closed, J*-closed, J**-closed and πJ*-closed.

References

[1] M. E. Abd EI-Monsef, S. N. EI-Deeb and R. A. Mahamoud, -open and -continuous mappings, Bull. Fac. Assut Univ. Sci. 12 (1983) 77.
[2] Arockiarani and C. Janaki, πgα-closed set and Quasi α-normal spaces, Acta Ciencia Indica. 33(2) (2007) 657-666.
[3] A. Aslim, A. Caksu Guler and T. Noiri, On πgs-closed sets in topological spaces, Acta Math. Hungar. 112 (2006) 275-283.
[4] J. Dontchev and M. Ganster., On δ- generalized closed sets and T3/4 spaces, Mem. Fac. Sci. Kochi. Univ.math. 17 (1996) 15-31.
[5] J. Dontchev and T. Noiri, Quasi-normal spaces and πg-closed sets, Acta Math. Hungar. 89(3) (2000) 211-219. Hamant Kumar / IJMTT, 68(2), 12-18, 2022 18
[6] H. Kumar, πgη-closed sets and some related topics, Jour. of Emerging Tech. and Innov. Res. 8(6) (2021) 367-374.
[7] N. Levine, Semi open sets and semi continuity in topological spaces, Amer. Math. Monthly. 70 (1963) 36-41.
[8] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo.19(2) (1970) 89-96.
[9] A. S. Mashour, On pre continuous and weak pre continuous functions, Pro.Math. Phys.Soc. Egypt, 53 (1982) 47-53.
[10] P. L. Meenakshi and K. Sivakamasundari, Unification of regular star open sets, International Journal of research and analytical reviews, Special Issue. 6 (2019) 20-23.
[11] P. L. Meenakshi and K. Sivakamasundari, J-closed sets in topological spaces, JETIR. 6 (2019) 193-201.
[12] P. L. Meenakshi and K. Sivakamasundari, J**-closed sets in topological spaces, Malaya Journal of Matematik, S(1) (2020) 206-213.
[13] O. Njastad, On some class of nearly open sets, Pacific. J. Math. , 15 (1965) 961-970.
[14] J. H. Park, On πgp-closed sets in topological spaces, Indian Journal of Pure and Appl. Math., 112 (2006) 257-283.
[15] S. Pious Missier and M. Annalakshmi, Between Regular Open Sets and Open Sets, IJMA.7(5) (2016) 128-133.
[16] N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (1968) 103-118.
[17] M. S. Sarsak and N. Rajesh, π-generalized semi-preclosed sets, International Mathematical Forum. 5(12) (2010) 573-578.
[18] M. H. Stone, Application of the theory of boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937) 375–481.
[19] R. Sudha and K. Sivakamasundari, δg*-closed sets in topological spaces, International Journal of Mathematical Archive, 3(3) (2012) 1222-1230.
[20] V. Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk SSSR. 178 (1968) 778-779.

Citation :

Hamant Kumar, "πJ*-Closed Sets in Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 2, pp. 12-18, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I2P503