| Summary: | 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.
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