Handbook of Analysis and Its Foundations: A Handbook Schechter, Eric

Eric Schechter (Autor)

ISBN 10: 0126227608 / ISBN 13: 9780126227604

Editore: Academic Press, 1996

This text provides an introduction to a wide range of topics in analysis including set theory and mathematical logic; algebra; toplogy; normed spaces; integration theory; toplogical vector spaces; and differential equations.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. "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 quite good - 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 Foundations of Analysis is a self-contained and unified handbook on the foundations of mathematical analysis. Intended as a self-study guide for advanced undergraduates and beginning graduate students in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Foundations of Analysis provides an introduction to a wide range of topics, includingset theory and mathematical logic, 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 in the presentation of classical pathological objects through nonconstructive proofs. More complete than any other book on the subject, students will find this to be an invaluable handbook. 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. Content: Sets and orderings: sets; functions; relations and orderings; more about sups and infs; sets of sets - filters topologies; 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: toplogical 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. Zusatzinfo references, index Sprache englisch Maße 200 x 242 mm Mathematik Informatik Mathematcs Mathe Informatiker Mathematische Analyse Analysis ISBN-10 0-12-622760-8 / 0126227608 ISBN-13 978-0-12-622760-4 / 9780126227604 In englischer Sprache. 883 pages. 24,2 x 19,8 x 4,6 cm. Codice articolo BN40752

Riassunto:

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. For more information on this book, see http://math.vanderbilt.edu/

Key Features
* 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/

Informazioni sull?autore: 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/

Dati bibliografici

Titolo: Handbook of Analysis and Its Foundations: A ...
Casa editrice: Academic Press
Data di pubblicazione: 1996
Legatura: Hardcover
Condizione: gut