Handbook of Analysis and Its Foundations

By

  • Eric Schechter, Vanderbilt University, Nashville, Tennessee, U.S.A.

Audience

Upper level undergraduate and graduate students in mathematics; practitioners and researchers in mathematics as well. Also, scientists with a beginning graduate level mathematics background.

 

Book information

  • Published: October 1996
  • Imprint: ACADEMIC PRESS
  • ISBN: 978-0-12-622760-4

Reviews

"This is quite a book! From the table of contents, it would appear to include just about everything one would want to know about the foundations of analysis. It is well-organized and the exposition in the sample chapters is quitegood?clear, concise, and relatively easy to read. It is very good technically; the author knows what he is talking about."
--George L. Cain, GEORGIA INSTITUTE OF TECHNOLOGY


"At the very outset, I would like to say that I am very much impressed by what I have seen. I have read the Preface and understood the authors purpose and his aims. I admire him for his courage in attempting such a daunting task, and I admire him even more for what appears to me to be a very successful completion of this task.....I am very excited over the prospect of this book being made available; it will be a very useful reference not only for beginning graduate students, but also for their teachers."
--Robert G. Bartle, EASTERN MICHIGAN UNIVERSITY



Table of Contents

Sets and Orderings: Sets. Functions. Relations and Orderings. More About Sups and Infs. Filters, Topologies, and Other Sets of Sets. Constructivism and Choice. Nets and Convergences. Algebra: Elementary Algebraic Systems. Concrete Categories. The Real Numbers. Linearity. Convexity. Boolean Algebras. Logic and Intangibles. Topology and Uniformity: Topological Spaces. Separation and Regularity Axioms. Compactness. Uniform Spaces. Metric and Uniform Completeness.Baire Theory. Positive Measure and Integration. Topological Vector Spaces: Norms. Normed Operators. Generalized Riemann Integrals. Frechet Derivatives. Metrization of Groups and Vector Spaces. Barrels and Other Features of TVSs. Duality and Weak Compactness. Vector Measures. Initial Value Problems. References. Subject Index. List of Symbols.