In their memoir “Representation
of rings by sections”, Memoirs, Amer. Math. Soc., Dauns and Hofmann introduce the
concept of “field of uniform spaces” which provides an extremely useful setting in
which a wide class of topological rings can be represented as rings of continuous
sections. The Dauns-Hofmann theory uses a mixture of uniform and topological
techniques to achieve its ends. The purpose of this note is to show that much of the
Dauns-Hofmann theory can be developed using solely topological techniques without
resort to the concept of field uniformity which is central to the Dauns-Hofmann
approach. The theory developed here represents a natural extension of that of fibre
bundles.
