Abstract
The set $\underline{SET}(n)$ 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 $\underline{SET}(n)$. Here, over the elements of $\underline{SET}(n)$ arithmetic operators of a topological type are defined and some of their basic properties are studied. Perspectives for future research are discussed.
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