Topological structures via MBJ-neutrosophic sets

Abstract

In this paper, we introduce the concept of quasi-coincidences in MBJ-neutrosophic sets and obtain
some of its properties. Also by defining the pre-image and the image of an MBJ-neutrosophic set under a
mapping, we confirm that their properties are naturally extensions of the classical case. Next, we define two
types of MBJ-neutrosophic neighborhood system and discuss their various properties and introduce the notion
of ◦-[resp. ∗-]MBJ-neutrosophic bases and deal with some of their properties. Finally, we define ◦-CI , ∗-CI ,
◦-CII and ∗-CII corresponding to the first countability and the second countability in classical topological
spaces, and we obtain the relationships between them