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$f_{\delta}$-Open Sets in Fine Topological Spaces

Document Type : Research Paper

Authors

1 Department of Mathematics and Computer Science, R.D. University, Jabalpur, India.

2 Department of Computer Science, College of Science, Cihan University-Duhok, Iraq.

3 Department of Mathematics, Faculty of Science, University of Zakho, Iraq.

Abstract

In this paper, the concept of $\delta$-cluster point on a set which belongs to the collection of fine open sets generated by the topology $\tau$ on $X$ has been introduced. Using this definition, the idea of $f_\delta$-open sets is initiated and certain properties of these sets have  also been studied. On the basis of separation axioms defined over fine topological space, certain types of $f_\delta$-separation axioms on fine space have also been  defined, along with some illustrative examples.

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References
[1] A. Al-Omari and T. Noiri, On operators in ideal minimal spaces, Mathematica, 58(81), (1-2), (2016), pp. 3–13.
[2] A. Al-Omari and T. Noiri, Operators in minimal spaces with hereditary classes, Mathematica, 61(84) (2), (2019), pp. 101-110.
[3] A. Al-Omari and T. Noiri, Properties of $\gamma H$-compact spaces with hereditary classes, Atti Accad. Peloritana Pericolanti, Cl. Sci. Fis. Mat. Nat., 98(2) (2020), A4 [11 pages].
[4] Z.A. Ameen, B.A. Asaad and R.A. Muhammed, On superclasses of $\delta$-open sets in topological spaces, Int. J. Appl. Math., 32(2) (2019), pp. 259-277.
[5] B.A. Asaad, T.M. Al-shami and E.A. Abo-Tabl, Applications of some operators on supra topological spaces, Demonstr. Math., 3(1) (2020), pp. 292-308.
[6] E. Ekici, On $a$-open sets, $A^*$-sets and decompositions of continuity and super continuity, Annales Univ. Sci. Budapes, 51 (2008), pp. 39–51.
[7] D. N. Georgiou, S. Jafari and T. Noiri, Properties of ($\Lambda$, $\delta$)-closed sets in topological spaces, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat., 8(7) (2004), pp. 745-756.
[8] S. Kasahara, Operation compact spaces, Math. Japonica, 24(1) (1979), pp. 97-105.
[9] G.S.S. Krishnan and K. Balachandran, On a class of $\gamma$-preopen sets in a topological space, East Asian Math. J., 22(2) (2006), pp. 131-149.
[10] G.S.S. Krishnan and K. Balachandran, On $\gamma$-semiopen sets in topological space, Bull. Cal. Math., 98(6) (2006), pp. 517-530.
[11] J. Munkres, Topology, Pearson New International Edition, Pearson, 2013.
[12] V. Popa and T. Noiri, On M-continuous functions, An. Univ. Dunarea de Jos Galati, Ser. Mat. Fiz. Mec. Teor. (2), 18(23) (2000), pp. 31-41.
[13] P.L. Powar, B.A. Asaad, K. Rajak and R. Kushwaha, Operation on Fine Topology, Eur. J. Pure Appl. Math., 12(3) (2019), pp. 960-977.
[14] P.L. Powar, T. Noiri and S. Bhadauria, On $\beta$-local Functions in Ideal topological Spaces, Eur. J. Pure Appl. Math., 13(4) (2020), pp. 758-765.
[15] P.L. Powar and K. Rajak, Fine-irresolute Mappings, J. Adv. Stud. Topol., 3(4) (2012), pp. 125-139.
[16] S. Raychaudhuri and M.N. Mukherjee, On $\delta$-almost continuity and $\delta$-preopen sets, Bull. Inst. Math. Acad. Sin., 21 (1993), pp. 357–366.
[17] N.V. Velicko, H-closed sets in topological spaces, Am. Math. Soc. Transl., 78 (1968), pp. 103–118.
Sahand Communications in Mathematical Analysis
Volume 21, Issue 1
January 2024
Pages 131-149
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