Topological MV-algebras

We introduce the notion of a topological MV-algebra and study its properties. We consider the completion under the I-adic topology. Various results are obtained analogous to those of topological rings. However, there are differences because MV-algebras are not rings, and results are obtained that do not correspond to results in topological rings. Some algebraic results are obtained from the topology, and the interactions between the algebra and the topology are studied.