| Description |
1 online resource (xxii, 883 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Bibliography |
Includes bibliographical references (pages 839-855) and index. |
| Note |
Print version record. |
| 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. |
| Summary |
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. |
| Language |
English. |
| Subject |
Mathematical analysis.
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Analyse mathématique.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Mathematical analysis
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| Indexed Term |
Calculus |
| Added Title |
Analysis and its foundations |
| Other Form: |
Print version: Schechter, Eric, 1950- Handbook of analysis and its foundations. San Diego, CA. : Academic Press, ©1997 0126227608 9780126227604 (DLC) 96032226 (OCoLC)35084403 |
| ISBN |
9780080532998 (electronic bk.) |
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0080532993 (electronic bk.) |
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1281054437 |
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9781281054432 |
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9786611054434 |
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661105443X |
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9780126227604 |
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0126227608 (alk. paper) |
| Standard No. |
AU@ 000048130847 |
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AU@ 000051562270 |
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AU@ 000054163204 |
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CHNEW 001007219 |
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DEBBG BV036962304 |
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DEBBG BV042317314 |
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DEBBG BV043137114 |
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DEBSZ 275196615 |
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DEBSZ 422177008 |
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GBVCP 802365124 |
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NZ1 12433443 |
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NZ1 15192865 |
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AU@ 000072977291 |
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