Abstract
Based on nano Z open set, we discuss and study about separation axioms, connectedness and compactness in a nano topological spaces. In this paper, the types of separation axioms such as \(\mathfrak {N} Z T_0\), \(\mathfrak {N} Z T_1\) and \(\mathfrak {N} Z T_2\) spaces are introduced and discuss in nano topological spaces. Also, nano Z regular space and nano Z normal space of nano Z open sets are established in nano topological spaces. Finally, nano Z compactness and nano Z connectedness are study and dealt with some properties in nano topological spaces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arul Selvaraj, X., Balakrishna, U.: \(Z\)-open Sets in Nano Topological Spaces. (Submitted).
Arul Selvaraj, X., Balakrishna, U.: Nano \(Z\)-Continuous Mappings and Homeomorphisms in Nano Topological Spaces. (Submitted).
EL-Magharabi, A.I., Mubarki, A.M.: \( Z \)-open sets and \( Z \)-continuity in topological spaces. International Journal of Mathematical Archive. 2 (10), 1819–1827 (2011).
Khalaf, M.M., Elmoasry, A.: Nano generalized closed sets and slightly Nano Separation Axioms. 11 (1), 91–98 (2015).
Lashin, E.F., Medhat, T.: Topological reduction of information systems. Chaos, Solitons and Fractals. 25, 277–286 (2015).
Lellis Thivagar, M., Richard, C.: On nano forms of weakly open sets. International Journal of Mathematics and Statistics Invention. 1, 31–37 (2013).
Pankajam, V., Kavitha, K.: \(\delta \) open sets and \(\delta \) nano continuity in \(\delta \) nano topological space. International Journal of Innovative Science and Research Technology. 2 (12), 110–118 (2017)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences. 11, 341–356 (1982).
Shalini, S.B.: A study on nano generalized \(\beta \) closed sets and its maps in nano topological spaces. Ph.D Thesis. Nirmala College for Women (A). Coimbatore, (2018).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Selvaraj, X.A., Balakrishna, U. (2022). Nano Z Seperation Axioms. In: Yilmaz, F., Queiruga-Dios, A., Santos Sánchez, M.J., Rasteiro, D., Gayoso MartÃnez, V., MartÃn Vaquero, J. (eds) Mathematical Methods for Engineering Applications. ICMASE 2021. Springer Proceedings in Mathematics & Statistics, vol 384. Springer, Cham. https://doi.org/10.1007/978-3-030-96401-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-96401-6_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-96400-9
Online ISBN: 978-3-030-96401-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)