Vol. 46, No. 2, 1973

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Fields of topological spaces

John Eldon Mack

Vol. 46 (1973), No. 2, 457–466

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.

Mathematical Subject Classification
Primary: 55F10
Received: 8 February 1972
Revised: 1 August 1972
Published: 1 June 1973
John Eldon Mack