Description

This version of Handbook of Analysis provides convenient access to reference material on the foundations of mathematical analysis. It is appropriate for advanced undergraduates and beginning graduate students in mathematics, as well as practitioners. The CD-ROM is a unified presentation of the foundation of virtually all of mathematics, with the exception of geometry.

Key Features

@introbul:Key Features @bul:* Topic areas included are: * Set theory and mathematical logic * Algebra * Topology * Normed spaces * Integration Theory * Topological Vector Spaces * Differential equations

Readership

Upper-level undergraduate and graduate students, as well as researchers and practitioners in mathematics.

Table of Contents

Preface. 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. Topology Vector Spaces. Norms. Normed Operators. Generalized Riemann Integrals. Fréchet Derivatives. Metrization Of Groups And Vector Spaces. Barrels And Other Features Of TVS's Duality And Weak Compactness. Vector Measures. Initial Value Problems. References. Index And Symbol List.

Details

Language:
English
Copyright:
© 1999
Published:
Imprint:
Academic Press
Print ISBN:
9780126227659
Electronic ISBN:
9780080925615

About the author

Eric Schechter

Eric Schechter obtained his Ph.D. in mathematics at the University of Chicago. He is currently Associate Professor at Vanderbilt University, and has also taught at Duke University. Schechters research focuses on differential equations, fixed point theory, and the Axiom of Choice. He currently resides in Nashville, Tennessee with his wife, Elvira Casal, and his two children. Please visit the web page for hisbook: http://math.vanderbilt.edu/~schectex/ccc/

Affiliations and Expertise

Vanderbilt University, Nashville, Tennessee, U.S.A.

Reviews

@from:Praise for the Book @qu:"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 understand the author's 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 task . . . The author has show considerable good judgment on which proofs to to include . . . So, I am very excited over the prospect of this book being made available; it will be a very useful reference both for beginning graduate students, but also for their teachers." @source:--BARTLE, MICHIGAN @qu:"From the table of contents, it would appear to include just about everything one would want to know about the foundation of analysis. It is well-organized and the exposition in the sample chapters is quite good--clear, concise, and relatively easy to read. It is very good technically; the author knows what he is talking about. . . A mini-encyclopedia it certainly is. . . It would be a fine reference book. . . It is a fine book indeed, written with care by a knowledgeable and thoughtful author." @source:--CAIN, GEORGIA TECH.