Universal covers of topological modules and a monodromy principle

Abstract

Let $R$ be a simply connected topological ring and $M$ be a topological left $R$-module in which the underling topology is path connected and has a universal cover. In this paper, we prove that a simply connected cover of $M$ admits the structure of a topological left $R$-module, and prove a Monodromy Principle, that a local morphism on $M$ of topological left $R$-modules extends to a morphism of topological left $R$-modules.