Some Properties of m-Pre-Topological Space

Abstract

This work presents a new class of topological space, namely m-topological spaces, is offered, and its properties are determined. Furthermore, we introduce and study the notion of m-pre-open, defined for topological spaces, and explore several of its essential characteristics in those regions. The m-pre-topological space  was constructed using  as the smallest structural space during this work. The study may also examine the topological characteristics and ramifications of m-pre-open structures. This could include discussions on closure operators, interior operators, and relationships with other open or closed sets that have been studied. Some operators of m-pre-open sets, as well as the m-pre-closure and m-pre-open alternative sets' interiors, were investigated in this research. In addition, the author may also analyze the behavior of m-pre-open sets under set operations like the union of sets ( ), the intersection of sets ( ), the complementation and their relationship with each other, and the effect of functions on them.