Foundations of Real and Abstract Analysis

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

Zusammenfassung
Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications.

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.