Techniques of Constructive Analysis / by Douglas S. Bridges, Luminiţa Simona Vîţă
(Universitext)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer New York |
| 出版年 | 2006 |
| 本文言語 | 英語 |
| 大きさ | XVI, 216 p. 10 illus : online resource |
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| 内容注記 | to Constructive Mathematics Techniques of Elementary Analysis The ?-Technique Finite-Dimensional and Hilbert Spaces Linearity and Convexity Operators and Locatedness |
|---|---|
| 一般注記 | This text provides a rigorous, wide-ranging introduction to modern constructive analysis for anyone with a strong mathematical background who is interested in the challenge of developing mathematics algorithmically. The authors begin by outlining the history of constructive mathematics, and the logic and set theory that are used throughout the book. They then present a new construction of the real numbers, followed by the fundamentals of the constructive theory of metric and normed spaces; the lambda-technique (a special method that enables one to prove many results that appear, at first sight, to be nonconstructive); finite- dimensional and Hilbert spaces; and convexity, separation, and Hahn-Banach theorems. The book ends with a long chapter in which the work of the preceding ones is applied to operator theory and other aspects of functional analysis. Many results and proofs, especially in the later chapters, are of relatively recent origin. The intended readership includes advanced undergraduates, postgraduates, and professional researchers in mathematics and theoretical computer science. With this book, the authors hope to spread the message that doing mathematics constructively is interesting and challenging, and produces new, deep computational information |
| 著者標目 | *Bridges, Douglas S. author Vîţă, Luminiţa Simona author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Functional analysis LCSH:Operator theory LCSH:Functions of real variables LCSH:Mathematical logic FREE:Mathematics FREE:Mathematical Logic and Foundations FREE:Analysis FREE:Real Functions FREE:Functional Analysis FREE:Operator Theory |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9780387381473 
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| ISBN | 9780387381473 |
| URL | http://dx.doi.org/10.1007/978-0-387-38147-3 |
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