This book represents a first course in the theory of metric, normed, and Hilbert spaces, and is intended (i) for mathematicians, physicists, and others who may need only one course that provides the elements of that subject, and (ii) as a foundation for more advanced courses in analysis, topology, and geometry for pure mathematicians. Prerequisites is a knowledge of the basic ideas of limits and continuity.

A wide range of material Clear and concise format Unique collection of nearly 750 exercises * Pointers to new branches of the subject

Autorentext

Prof. Douglas S. Bridges is a professor of pure mathematics at the University of Canterbury. His research interests include the constructive foundations of analysis and topology; mathematical economics; computability and abstract complexity theory; and quantum logic. He has published many related articles and papers, among his 8 authored books are "Computability: A Mathematical Sketchbook", "Foundations of Real and Abstract Analysis", and "Techniques of Constructive Analysis". He is a Fellow of the Royal Society of New Zealand, and a Corresponding Fellow of the Royal Society of Edinburgh. Dr. Lumini a Simona Vî is an Adjunct Fellow of the Department of Mathematics and Statistics, University of Canterbury, and a Senior Business Analyst with the New Zealand Customs Service. Her research interests include constructive foundations of analysis and topology, and recursive function theory, computability and complexity. She has published many related articles and papers, and coauthored "Techniques of Constructive Analysis".

Inhalt
Real Analysis.- Analysis on the Real Line.- Differentiation and the Lebesgue Integral.- Abstract Analysis.- Analysis in Metric Spaces.- Analysis in Normed Linear Spaces.- Hilbert Spaces.- An Introduction to Functional Analysis.