Introduction to Abstract Analysis (Dover Books on Mathematics)

Developed from lectures delivered at NASA's Lewis Research Center, this concise text introduces scientists and engineers with backgrounds in applied mathematics to the concepts of abstract analysis. Rather than preparing readers for research in the field, this volume offers background necessary for reading the literature of pure mathematics.
Starting with elementary set concepts, the treatment explores real numbers, vector and metric spaces, functions and relations, infinite collections of sets, and limits of sequences. Additional topics include continuity and function algebras, Cauchy completeness of metric space, infinite series, and sequences of functions and function spaces. The relation between convergence and continuity and algebraic operations is discussed in the abstract setting of linear spaces in order to acquaint readers with these important concepts in a fairly simple way. Detailed, easy-to-follow proofs and examples illustrate how the material relates to and serves as a foundation for more advanced subjects.

Marvin E. Goldstein was a scientist at Lewis Research Center in Cleveland when this book was published by NASA in 1969. He was the Chief Scientist at NASA's Glenn Research Center from 1980 to 2004, taught at Case Western Reserve University and MIT, and wrote more than 120 scientific and mathematical papers. Burt M. Rosenbaum worked in applied mathematics at NASA's Lewis Research Center from 1957 to 1973 and taught at Cleveland State University.