By J. R. Isbell
Uniform areas play an identical position for uniform continuity as topological areas for continuity. the speculation was once created in 1936 through A. Weil, whose unique axiomatization was once quickly by way of these of Bourbaki and Tukey; during this booklet use is made mainly of Tukey's process, in line with uniform coverings. The association of the ebook as a complete depends upon the Eilenberg-MacLane notions of class, functor and naturality, within the spirit of Klein's Erlanger software yet with better succeed in. The preface provides a concise background of the topic considering that 1936 and a foreword outlines the class concept of Eilenberg and MacLane. The chapters conceal primary innovations and buildings; functionality areas; mappings into polyhedra; measurement (1) and (2); compactifications and in the community nice areas. many of the chapters are via workouts, occasional unsolved difficulties, and an immense unsolved challenge; the recognized notable challenge of characterizing the Euclidean aircraft is mentioned in an appendix. there's a sturdy index and a copious bibliography meant to not itemize resources yet to lead extra studying.
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