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# ðŸ“™ Uniform spaces by J. R. Isbell â€” epub download

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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-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

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- Series:
**Mathematical Surveys and Monographs 012** - Author:
**J. R. Isbell** - Year:
**1964** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0-8218-1512-1,978-0-8218-1512-0,31-1952-189-2,107-1963-38-4,42-1957-479-4,71-1951-152-1,68-1962-609-6**

- DPI:
**600** - File size:
**2 824 862** - Format:
**djvu**

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â€‹This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about ...

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 T...

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-...

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-...

This tract provides a compact introduction to the theory of proximity spaces and their generalisations, making the subject accessible to readers having a basic knowledge of topological and uniform spaces, such as can be found in standard textbooks. Two ch...

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-...

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-...

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-...

This book is based on lectures I have given to senior undergraduate and graduate audiences at Oxford and elsewhere over the years. My aim has been to provide an outline of both the topological theory and the uniform theory, with an emphasis on the relatio...