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RT Book, Whole SR Electronic DC OPAC T1 Techniques of Constructive Analysis / by Douglas S. Bridges, Luminiţa Simona Vîţă T2 Universitext A1 Bridges, Douglas S. A1 Vîţă, Luminiţa Simona A1 SpringerLink (Online service) YR 2006 FD 2006 SP XVI, 216 p. 10 illus K1 Mathematics K1 Mathematical analysis K1 Analysis (Mathematics) K1 Functional analysis K1 Operator theory K1 Functions of real variables K1 Mathematical logic K1 Mathematics K1 Mathematical Logic and Foundations K1 Analysis K1 Real Functions K1 Functional Analysis K1 Operator Theory PB Springer New York PP New York, NY SN 9780387381473 LA English (英語) CL DC23:511.3 NO 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 NO 書誌ID=1003000778; LK [E Book]http://dx.doi.org/10.1007/978-0-387-38147-3 OL 30