Foundations of Real and Abstract Analysis (1998)

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.