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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | EB000056 | EB 000056 | Electronic Book | 1:EBOOK | Searching... |
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Summary
Summary
This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces and with associated results about operators and their adjoints on a Hilbert space. The first appendix gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. No background in intuitionistic logic or constructive analysis is needed in order to read the book, but some familiarity with the classical theories of metric, normed and Hilbert spaces is necessary.
Reviews 1
Choice Review
Bridges and Vita (both, Univ. of Canterbury, New Zealand) offer a book, written jointly by an associate (Bridges) of the famous Errett Bishop, widely hailed as the founder of modern constructive analysis, and by his one-time post-doctoral student (Vita). Topics come less from calculus and more from higher-functional analysis (metric spaces, convexity in normed linear spaces, Hahn-Banach and separation theorems, operators and their adjoints, and open mapping, inverse mapping, and closed-graph theorems). The direction taken provides tools and techniques to surmount hurdles that constructivist requirements place in the path that a more-traditionalist approach might follow. The resulting impression is that constructivist analysis is an arcane specialty, fraught with unexpected difficulties and requiring great technical proficiency, perhaps best left to experts like Bridges (with more than two dozen of his own works listed among the references, including his joint monograph with Bishop). Not nearly as well conveyed to the reader as in Mark Bridger's more elementary recent Real Analysis: A Constructive Approach (CH, Aug'07, 44-6891), is the message that the constructivist approach is actually more natural and defensible than the traditional approach. Thorough index; plentiful exercises and references. Eminently suitable. Summing Up: Recommended. Upper-division undergraduates through faculty. F. E. J. Linton emeritus, Wesleyan University
