An Introduction to Analysis

This book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form it has been used in this way at the University of Michigan, Indiana University, and Texas A&M University. The book addresses the needs of a beginning graduate student, that is a student who has completed an undergraduate program with a mathematics major.
TOC: Contents: The rudiments of set theory.- Number systems.- Linear analysis.- Cardinal numbers.- Ordinal numbers.- Metric spaces.- Continuity and limits.- Completeness and compactness.- General topology.- Bibliography.- Index.