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Uniform Spaces
 
Uniform Spaces
Softcover ISBN:  978-0-8218-1512-0
Product Code:  SURV/12
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1240-1
Product Code:  SURV/12.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1512-0
eBook: ISBN:  978-1-4704-1240-1
Product Code:  SURV/12.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Uniform Spaces
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Uniform Spaces
Softcover ISBN:  978-0-8218-1512-0
Product Code:  SURV/12
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1240-1
Product Code:  SURV/12.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1512-0
eBook ISBN:  978-1-4704-1240-1
Product Code:  SURV/12.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 121964; 175 pp
    MSC: Primary 54

    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-Mac Lane 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 Mac Lane. 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.

  • Table of Contents
     
     
    • Chapters
    • I. Fundamental concepts
    • II. Fundamental constructions
    • III. Function spaces
    • IV. Mappings into polyhedra
    • V. Dimension (1)
    • VI. Compactifications
    • VII. Locally fine spaces
    • VIII. Dimension (2)
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 121964; 175 pp
MSC: Primary 54

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-Mac Lane 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 Mac Lane. 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.

  • Chapters
  • I. Fundamental concepts
  • II. Fundamental constructions
  • III. Function spaces
  • IV. Mappings into polyhedra
  • V. Dimension (1)
  • VI. Compactifications
  • VII. Locally fine spaces
  • VIII. Dimension (2)
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.