Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect

The set SET(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [4], some arithmetic functions and arithmetic operators of a modal type are defined over the elements of SET(n). Here, over the elements of SET(n) arithmetic operators of a topological type are defined and some of their basic properties are studied. Perspectives for future research are discussed.

Automated summary

This paper introduces a set SET(n) generated by an arbitrary natural number n, and defines some arithmetic functions and operators of a modal type on the elements of SET(n) as described in [3] and [4]. Additionally, it defines arithmetic operators of a topological type on the elements of SET(n) and studies some of their basic properties. Perspectives for future research are also discussed.