Nano ∧ β -sets and nano ∧ β -continuity

• Main Author: M. Hosny
• Format: Article
• Language: English
• Published: SpringerOpen 2020-04-01
• Series: Journal of the Egyptian Mathematical Society
• Subjects: Nano topology; Nano ∧ β -sets; Nano ∧ β -continuity
• Online Access: http://link.springer.com/article/10.1186/s42787-020-0070-5

Abstract The concept of nano near open sets was originally proposed by Thivagar and Richard (Int. J. Math. Stat. Inven 1:31-37). The main aspect of this paper is to introduce a new sort of nano near open sets namely, nano ∧ β -sets. Fundamental properties of these sets are studied and compared to the previous one. It turns out that every nano β-open set is a nano ∧ β -set. So, nano ∧ β -sets are an extension of the previous nano near open sets, such as nano regular open, nano α-open, nano semi-open, nano pre-open, nano γ-open, and nano β-open sets. Meanwhile, it is shown that the concepts of nano ∧ β -sets and nano δβ-open sets are different and independent. Based on these new sets, nano ∧ β -continuous functions are defined and some results involving their characterizations are derived. In addition, the concepts of nano ∨ β -closure and nano ∧ β -interior are presented. Their properties are used to introduce and study the nano ∧ β -continuous functions.