Topological Uniform Structures (Dover Books on Mathematics) by Warren Page (PDF)

Description

Proofs are detailed and carefully done … there is a lot of fine material in this book. — Bulletin of the American Mathematical Society.While many sources offer partial coverage of uniform spaces, topological groups, topological vector spaces, topological algebras, and abstract harmonic analysis, this graduate-level text was the first to give a thorough and fully detailed account of all these topics. It also contains a section on vector-valued measure spaces as well as numerous problems and examples. Chief among the salient features of the work is its overall unifying theme of topologies compatible with increasingly enriched algebraic structures. The book gradually deepens the reader’s appreciation of the rich interplay among diverse areas of mathematics. Each section begins with a brief summary of the important points to appear, and the theory unfolds smoothly through an abundance of relevant commentary and well-chosen examples.In addition, the remarks that follow most theorems and examples are replete with useful information, counterexamples, and other points worth noting. Finally, each section ends with a set of problems (more than 220, with several subparts in each).Largely self-contained and accessible to students with a background in elementary analysis, linear algebra, and point set topology, the book nevertheless covers a good deal of advanced material. However, because of its readability, leisurely pace, and highly illustrative contents, it is an ideal reference for advanced undergraduates and beginning graduate students.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I bought this book as a reference on uniform spaces. It turned out to have much more than this: topological groups and other topics in modern mathematics are also treated in deep detail, giving this book a fantastic amount of information per dollar.I was however disappointed with the poor work made by typesetters and proofreaders: this goes from misreferencing theorems and examples, to using the “element of” in place of “subset of” sign! This I believe to be unacceptable in a university level book, and is the reason why I only give it three stars. If you are more tolerant than me from this point of view, you might consider it a four or even five star title.

⭐Nice and valuable book in topological groups.

⭐

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