α(gg)*-Closed Sets in Topological Spaces

T. Shyla Isac Mary; G. Abhirami

doi:https://doi.org/10.14445/22315373/IJMTT-V68I3P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 3 | Year 2022 | Article Id. IJMTT-V68I3P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I3P502

α(gg)*-Closed Sets in Topological Spaces

T. Shyla Isac Mary, G. Abhirami

Citation :

T. Shyla Isac Mary, G. Abhirami, "α(gg)*-Closed Sets in Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 3, pp. 5-10, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I3P502

Abstract

In this paper we introduce the concept of alpha generalization of generalized star closed sets in topological spaces. Also, we investigated its relation among other closed sets. Further, we derived some of its characteristics.

Keywords

α(gg)*-closed sets, (gg)*-open sets, α-closure.

References

[1] Ahmad-Al-Omari and Mohd.Salmi Md Noorani, on Generalized B-Closed Sets, Bulletin of Mathematical Sciences Society, 32 (2009) 19-30.
[2] D. Andrijevic, Semi Pre-Open Sets, Mat. Vesnik, 48 (1986) 24-32.
[3] D. Andrijevic, B-Open Sets, Mat. Vesnik, 48 (1996) 59-64.
[4] S. P. Arya, and T. M. Nour, Characterizations of S-Normal Spaces, Indian J. Pure. Appl. Math., 21(8) (1990) 717-719.
[5] Basavaraj, M.Ittangi and H. G. Govardhana Reddy, on Gg-Closed Sets in Topological Spaces, Int. J. of Mathematical Archive, 8(8) (2017) 126-133.
[6] Basavaraj, M.Ittangi and Veeresha. A. Sajjanar, On Weakly Semi-Closed Sets in Topological Spaces, Int. J. of Mathematical Archive, 8(9) (2017) 126-134.
[7] S. S. Benchalli and R. S. Walli, On RW-Closed Sets in Topological Spaces, Bull. Malaysian. Math. Sci. Soc., (2) 30(2) (2007) 99-110.
[8] P. Bhattacharya and B. K. Lahiri, Semi-Generalized Closed Sets on Topology, Indian. J. Math 29(3) (1987) 375-382.
[9] D. E. Cameron, Properties of S-Closed Spaces, Proc. Amer. Math. Soc., 72 (1978) 581-586.
[10] I. Christal Bai and T. Shyla Isac Mary, (Gg)*-Closed Sets in Topological Spaces, International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(4) (2018) 395-403.
[11] J. Dontchev, On Generalizing Semi-Pre-Open Sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 16 (1995) 35-48.
[12] L. Elvina Mary and R. Myvizhi, (Gs)*-Closed Sets in Topological Spaces, International Journal of Mathematics Trends and Technology-7(2) (2014) 83-93.
[13] Y. Gnanambal, On Generalized Pre Regular Closed Sets in Topological Spaces, Indian J. Pure. Appl. Math., 28(3) (1997) 351-360.
[14] C. Janaki and Renu Thomas, On R* Closed Sets in Topological Spaces, International Journal of Mathematical Archive, 3(8) (2012) 3067-3074.
[15] N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. Math. Monthly, 70 (1963) 36-41.
[16] N. Levine, Generalized Closed Sets in Topology, Rend. Circ. Mat. Palermo, 19(2) (1970) 90-96 .
[17] H. Maki, R. Devi and K. Balachandran, Associated Topologies of Generalized α-Closed Sets and α-Generalized Closed Sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 15 (1994) 51-63.
[18] A.S. Mashour, M.E. Abd El-Monsef and S.N. El-Deeb, On Pre-Continuous and Weak Pre-Continuous Mappings, Proc. Math and Phy. Soc. Egypt, 53(1963) 47-53.
[19] G.B. Navalagi and Chandrashekarappa, On Gspr-Closed Sets in Topological Spaces, 2 (1-2) (2010) 35-44.
[20] O.Njastad, On Some Classes of Nearly Open Sets, Pacific. J. Math., 15 (1965) 961-970.
[21] R. Parimelazhagan and D. Vidhya, G*B-Closed Sets in Topological Spaces, Int. J. Contemp. Math. Sciences. 7(27) (2012) 1305-1312.
[22] A. Parvathi and P. Priyadharshini, A Study on G*Bω-Closed Sets in Topological, Bitopological and Tritopological Spaces, Ph.D Thesis, Avinashilingam Deemed University For Women Coimbatore (2016).
[23] M. Pauline Mary Helen and A. Gayathri, Ĝ*-Closed Sets in Topological Spaces, International Journal of Mathematics Trends and Technology, 6(2) (2014) 60-74.
[24] M. Pauline Mary Helen and A. Kulandhai Therese, (Gsp)*-Closed Sets in Topological Spaces, International Journal of Mathematics Trends and Technology, 6 (2014) 75-86.
[25] S. Pious Missier and M. Anto, Ĝ*S-Closed Sets in Topological Spaces, International Journal of Modern Engineering Research, 4(11) (2014) 32-38.
[26] P. Pushpalatha and K. Anitha, G*S-Closed Sets in Topological Spaces, Int. J. Contemp. Math. Sciences. 6(19) (2011) 917-929.
[27] Saeid Jaifari, M. Lellis Thivagar and Nirmala Rebecca Paul, Remarks on Gα~ -Closed Sets in Topological Spaces, Int. Mathematical Forums, 5(24) (2010) 1167-1178.
[28] S. Sekar & G. Kumar, On GαrClosed Sets in Topological Spaces, International Journal of Pure and Applied Mathematics, 108(4) (2016) 791-800.
[29] M. Sheik John, On W-Closed Sets in Topology, Acta Ciencia Indica, 4 (2000) 389-392.
[30] M. Stone, Applications of the Theory of Boolean Rings To General Topology, Trans. Amer. Maths. Soc., 41 (1937) 374-481.
[31] A. Vadivel and K.Vairamanickam, Rgα-Closed Sets and Rgα-Open Sets in Topological Spaces, Int. J. of Math. Analysis, 3(37) (2009) 1803-1819.
[32] M. K. R. S. Veerakumar, Between G*-Closed Sets and G-Closed Sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 21 (2000) 1-19.
[33] M. K. R. S. Veerakumar, On α-Generalized Regular Closed Sets, Indian. J. of Math, 44(2) (2002) 165-181.
[34] M. K. R. S. Veerakumar, G#-Closed Sets in Topological Spaces, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 24 (2003) 1-13.
[35] V. Zaitsav, On Certain Classes of Topological Spaces and Their Bicompactifications, Dokl. Akad. Nauk Sssr, 178 (1968) 778-779.