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Modern Analysis and Topology (Universitext)By Norman R. Howes
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The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background. An advanced calculus course and an introductory topology course should be adequate. But it is also intended that this book be able to take the reader from that state to the frontiers of modern analysis and topology in-so-far as they can be done within the framework of uniform spaces. Modern analysis is usually developed in the setting of metric spaces although a great deal of harmonic analysis is done on topological groups and much offimctional analysis is done on various topological algebraic structures. All of these spaces are special cases of uniform spaces. Modern topology often involves spaces that are more general than uniform spaces, but the uniform spaces provide a setting general enough to investigate many of the most important ideas in modern topology, including the theories of Stone-Cech compactification, Hewitt Real-compactification and Tamano-Morita Para compactification, together with the theory of rings of continuous functions, while at the same time retaining a structure rich enough to support modern analysis.
- Sales Rank: #2366641 in Books
- Published on: 2013-10-04
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.00" w x 6.10" l, 1.41 pounds
- Binding: Paperback
- 444 pages
Review
"...recommended both to experts and novices...extremely useful for instructors teaching advanced abstract analysis and topology courses." -- ACTA SCIENTIARUM MATHEMATICARUM
From the Back Cover
The book presents an integrated treatment of general topology and real analysis. The integration mechanism is the concept of a uniform space. Uniform spaces have enough structure to support modern analysis. At the same time they are general enough to include those spaces in which the most important developments of modern topology have occurred. The book is intended to take a reader of modest background to the frontiers of modern analysis and topology insofar as these disciplines can be done within the framework of uniform spaces. This book is intended to interest the expert as well as the novice. The book records many recent solutions to long-standing problems in both these areas and raises several new problems.
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