Techniques of Constructive Analysis (Universitext)
Techniques of Constructive Analysis by Douglas S. Bridges, published by Springer on September 19, 2006, is a comprehensive introduction to constructive mathematics. This edition spans 231 pages and is presented in English. The book emphasizes techniques and results from the last two decades, specifically focusing on developments in Bishop-style constructive analysis.
Readers will find a thorough exploration of fundamental theories related to the real line and metric spaces, with particular attention to locatedness in normed spaces and the implications for operators and their adjoints on Hilbert spaces. The text includes two appendices that provide essential concepts about sets and orders, as well as the axioms for intuitionistic logic. While no prior knowledge of intuitionistic logic or constructive analysis is required, a basic understanding of classical theories concerning metric, normed, and Hilbert spaces is necessary for a complete grasp of the material.
Official synopsis Publisher
This book is an introduction to constructive mathematics with an emphasis on techniques and results that have been obtained in the last twenty years. It is the only book to deal with developments in Bishop-style constructive analysis over the past 20 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. There are two appendices to the book. The first gathers together some basic notions about sets and orders; the second gives the axioms for intuitionistic logic. The intended readership of the book consists of senior undergraduate and graduate students, as well as professional research mathematicians. 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.
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