The Macias topology on integral domains

Abstract

In this manuscript, a recent topology on the positive integers, generated by the collection of relatively prime positive integers, is generalized over integral domains. Some of its topological properties are studied. Properties of this topology on infinite principal ideal domains that are not fields are also explored, and a new topological proof of the infinitude of prime elements is obtained (assuming the set of units is finite), different from those presented in the style of H. Furstenberg. Finally, some problems are proposed.