Nano S_β-Connectedness in Nano Topological Spaces




Nano S_β-open sets, Nano S_β-connected, Nano S_β-hyperconnected, Nano S_β-ultraconnected


The aim of this study is to introduce the notions of nano Sβ-connected, nano Sβ-hyperconnected and nano Sβ-ultraconnected by using all forms of nano Sβ-open sets in nano topological spaces. Then, we study their relationship and show that if a nano topological space is nSβ-connected, W is also nano connected space but not the converse. Also, we study each notion in terms of upper, lower, and boundary approximations.


Revathy, And G. Ilango., On nano β-open sets. Int. J. Eng. Contemp. Math. Sci, 1, 2, 1-6, 2015.

M. L. Thivagar, And I. G. Antoinette, Note on nano hyperconnected spaces. South east Asian journal of Mathematics and Mathematical sciences, 15, 1, 25-36, 2019.

M. L. Thivagar, And C. Richard, On nano forms of weakly open sets. International journal of mathematics and statistics invention, 1, 1, 31-37, 2013.

O. T. Pirbal, and N. K. Ahmed, On nano Sβ-open sets in nano topological spaces. General Letters in Mathematics, 12, 1, 23-30, 2022.


O. T. Pirbal, and N. K. Ahmed, A new type of nano semi open sets in nano topological spaces. MSc Thesis, Salahaddin University-Erbil. 2022.


N. K. Ahmed and O. T. Pirbal, Nano SC-open sets in nano topological spaces. Ibn Al-Haitham Journal for Pure and Applied Sciences, Accepted. 2023.

Z. Pawlak, Rough sets. International journal of computer & information sciences, 11, 5, 341-356, 1985.





Submission Dates

Received: 02/12/2022

Revised: 11/12/2022

Accepted: 31/01/2023

How to Cite

N. K. . Ahmed and O. T. Pirbal, “Nano S_β-Connectedness in Nano Topological Spaces”, Al-Mustansiriyah Journal of Science, vol. 34, no. 2, pp. 87–94, Jun. 2023.