By J. R. Isbell
Uniform areas play a similar position for uniform continuity as topological areas for continuity. the speculation used to be created in 1936 by way of A. Weil, whose unique axiomatization was once quickly through these of Bourbaki and Tukey; during this booklet use is made mainly of Tukey's method, in line with uniform coverings. The association of the ebook as an entire is dependent upon the Eilenberg-MacLane notions of type, functor and naturality, within the spirit of Klein's Erlanger application yet with better succeed in. The preface provides a concise historical past of the topic considering the fact that 1936 and a foreword outlines the class conception of Eilenberg and MacLane. The chapters hide primary thoughts and structures; functionality areas; mappings into polyhedra; measurement (1) and (2); compactifications and in the community nice areas. many of the chapters are via routines, occasional unsolved difficulties, and an important unsolved challenge; the well-known striking challenge of characterizing the Euclidean airplane is mentioned in an appendix. there's a sturdy index and a copious bibliography meant to not itemize resources yet to steer extra interpreting.