Techniques of Constructive Analysis [Paperback]

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.

This book is an introduction to constructive mathematics with an emphasis on techniques and results that have been obtained in the last twenty years. There is specific focus on techniques and themes, and the book includes many simplified or improved proofs.

From the reviews:

Constructive mathematics is often mistakenly thought to be a branch of formal logic, or to involve recursive function theory. The recent Bridges-V?ta textbook is an exemplar of perseverance in efforts to correct this situation. For students at the graduate level it is an excellent introduction to constructive mathematics: for the more experienced reader it is a portal to some of the latest research using constructive methods. (Mark Mandelkern, Zentralblatt MATH, Vol. 1107 (9), 2007)

Bridges and Vita (both, Univ. of Canterbury, New Zealand) offer a book, written jointly by an associate (Bridges) of the famous Errett Bishop & . Thorough index; plentiful exercises and references. Eminently suitable. Summing Up: Recommended. Upper-division undergraduates through faculty. (F. lSÃ