AMS Bookstore LOGO amslogo
Return to List  Item: 1 of 1   
Uniform Spaces
J. R. Isbell

Mathematical Surveys and Monographs
1964; 175 pp; softcover
Volume: 12
Reprint/Revision History:
reprinted with corrections 1986; third printing 1991
ISBN-10: 0-8218-1512-1
ISBN-13: 978-0-8218-1512-0
List Price: US$46
Member Price: US$36.80
Order Code: SURV/12
[Add Item]

Request Permissions

Uniform spaces play the same role for uniform continuity as topological spaces for continuity. The theory was created in 1936 by A. Weil, whose original axiomatization was soon followed by those of Bourbaki and Tukey; in this book use is made chiefly of Tukey's system, based on uniform coverings.

The organization of the book as a whole depends on the Eilenberg-MacLane notions of category, functor and naturality, in the spirit of Klein's Erlanger Program but with greater reach. The preface gives a concise history of the subject since 1936 and a foreword outlines the category theory of Eilenberg and MacLane. The chapters cover fundamental concepts and constructions; function spaces; mappings into polyhedra; dimension (1) and (2); compactifications and locally fine spaces. Most of the chapters are followed by exercises, occasional unsolved problems, and a major unsolved problem; the famous outstanding problem of characterizing the Euclidean plane is discussed in an appendix. There is a good index and a copious bibliography intended not to itemize sources but to guide further reading.

Powered by MathJax
Return to List  Item: 1 of 1   

  AMS Home | Comments:
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia