Handbook of Analysis and Its Foundations by Eric SchechterHandbook of Analysis and Its Foundations by Eric Schechter

Handbook of Analysis and Its Foundations

byEric Schechter, Eric Schechter

Other | October 24, 1996

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Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook.

  • Covers some hard-to-find results including:

  • Bessagas and Meyers converses of the Contraction Fixed Point Theorem

    Redefinition of subnets by Aarnes and Andenaes

    Ghermans characterization of topological convergences

    Neumanns nonlinear Closed Graph Theorem

    van Maarens geometry-free version of Sperners Lemma

  • Includes a few advanced topics in functional analysis

  • Features all areas of the foundations of analysis except geometry

  • Combines material usually found in many different sources, making this unified treatment more convenient for the user

  • Has its own webpage: http://math.vanderbilt.edu/

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 wi...
Title:Handbook of Analysis and Its FoundationsFormat:OtherDimensions:883 pages, 1 × 1 × 1 inPublished:October 24, 1996Publisher:Elsevier ScienceLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0080532993

ISBN - 13:9780080532998


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.