Nano δI-closed Sets in Nano Ideal Topological Spaces

Authors

  • M.Karthigai Jothi Manonmaniam Sundaranar University, Tirunelveli
  • K Palani Manonmaniam Sundaranar University, Tirunelveli

DOI:

https://doi.org/10.23755/rm.v48i0.1204

Keywords:

nano δI-open sets, nano δI-closed sets, nano ideal topological space.

Abstract

This article investigates the notion of N-δI-closed sets and its properties in ideal nano topological space using the closure operator NclδI(S)={xÎՍ/ Nint(Ncl*(W))∩ S ≠ ∅, for each WÎWN(x)}. We establish NclδI(S) is the intersection of all N-δI-closed supersets of S and NintδI(S) is the union of all N-δI-open subsets of S in this space. Apart from that N-δI-closed sets occurs between the class of Nδ-closed sets and N-closed sets. Moreover, we explore the concepts of N-δI-interior, N-δI-Exterior, N-δI-Border, and N-δI-Frontier and discuss its properties.

Author Biographies

  • M.Karthigai Jothi, Manonmaniam Sundaranar University, Tirunelveli
    Research Scholar, Reg. No: 21212012092005, PG and Research Department of Mathematics, A.P.C. Mahalaxmi College for Women, Thoothukudi-628003, Tamil Nadu, India, jothiperiyasamy05@gmail.com, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli -627012. Tamilnadu, India.
  • K Palani, Manonmaniam Sundaranar University, Tirunelveli
    Associate Professor and Head, PG and Research Department of Mathematics, A.P.C. Mahalaxmi College for Women, Thoothukudi-628003, Tamil Nadu, India, palani@apcmcollege.ac.in, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli -627012. Tamilnadu, India

References

D. Jankovic and T.R. Hamlet, New topologies from old via ideals. Amer. Math. Monthly, 295–310, 1990.

K. Kuratowski, Topology, Academic Press, New York, Vol.1: 1996.

M. Lellis Thivagar, and Carmel Richard, On Nano forms of weakly open sets, Mathematical Theory and Modeling, 3(7): 32-37, 2013.

M. Lellis Thivagar and C. Richard, On Nano Continuity, International Journal of Mathematics and Statistics Invention, 1(1): 31–37, 2013.

M. Parimala, T. Noiri and S. Jafari, New types of nano topological spaces via nano ideals, Research Gate, 1–10, 2016.

M. Parimala, J. Sathiyaraj and V. Chandrasekar, New notions via nano δ-open sets with an application in diagnosing people with type-II diabetes, Advances in Mathematics: Scientific Journal, 3: 1247–1253, 2020.

M. Parimala and R. Perumal, a weaker form of open sets in nano ideal topological spaces, Global Journal of Pure and Applied Mathematics (GJPAM), 12(1): (2016).

M. Parimala and S. Jafari, On some new notions in nano ideal topological spaces, Eurasian Bulletin of Mathematics, 1(3): 89–96, 2018.

R. Premkumar and M. Rameshpandi, New sets in ideal nano topological spaces, Bull. int. Math. Virtual. Inst. Vol. 10(1): 19–27,2020.

C. Richard, Studies on nano topological spaces, Ph.D. Thesis, Madurai Kamaraj University, Indi, 2013.

S. Yuksel, A. Acikgoz and T. Noiri, On δ-I-Continuous Functions, Turk. J. Math. 29: 39–51, 2005.

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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