Introduction to Abelian Spaces: A Connection with Topology

Abstract

An abelian group is an algebraic property of an algebraic structure, but it can also be considered as a metric space. This paper establishes a new concept ``Abelian Space'', a space containing a set and an operator which is not only an abelian group, but can also be viewed as a metric space. In this paper, with reference to the symmetric difference operator between two sets, it is proved that an abelian group can also be considered as an abelian ``metric'' space.