LaTeX file is available for download. This book provides a unified development of analysis and topology. These two subjects are studied in the context of uniform spaces. Much of modern analysis is done within the framework of normed linear spaces or of topological groups.
Uniform spaces provide the common thread that connects normed spaces and topological groups.
Although the ideas in the introduction and parts of Chapter 1 are elementary and easily within the reach of beginning graduate students, most of this book requires some advanced knowledge. The reader, who does not have the helpful guidance of an instructor, needs to be comfortably at ease in dealing with locally finite covers, with refinements of covers and with similar ideas. One of the strengths of the book is its description, in Chapter 6, of the very useful and elegant contributions of Professors K. Morita and H. Tamano. This book represents the first time that these results have been assembled together in one place. Mathematics is blessed with three distinct but equivalent definitions of uniform spaces.