Softcover ISBN: | 978-0-8218-1512-0 |
Product Code: | SURV/12 |
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AMS Member Price: | $103.20 |
eBook ISBN: | 978-1-4704-1240-1 |
Product Code: | SURV/12.E |
List Price: | $125.00 |
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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 |
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 |
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Book DetailsMathematical Surveys and MonographsVolume: 12; 1964; 175 ppMSC: 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.
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Table of Contents
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Chapters
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I. Fundamental concepts
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II. Fundamental constructions
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III. Function spaces
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IV. Mappings into polyhedra
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V. Dimension (1)
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VI. Compactifications
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VII. Locally fine spaces
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VIII. Dimension (2)
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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)