Handbook of Analysis and Its Foundations

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Handbook of Analysis and Its Foundations by Eric Schechter, Elsevier Science
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Author: Eric Schechter ISBN: 9780080532998
Publisher: Elsevier Science Publication: October 24, 1996
Imprint: Academic Press Language: English
Author: Eric Schechter
ISBN: 9780080532998
Publisher: Elsevier Science
Publication: October 24, 1996
Imprint: Academic Press
Language: English

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/

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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.

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