This text assumes no knowledge of mathematical logic. Beginning with a nonstandard construction of the real number system, it leads students thorough the basic topics of elementary real analysis, topological spaces, and Hilbert space. Includes nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. 1977 edition. Unabridged republication of the edition published by John Wiley & Sons, Inc., New York, 1977.
Here's a sample of other books in this Dover category
Introduction to Analysis by Maxwell Rosenlicht Unusually clear, accessible coverage of set theory, real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, more. Wide range of problems. Written for junior and senior undergraduates. Bibliography.
Nonstandard Methods in Stochastic Analysis and Mathematical Physics by Sergio Albeverio, Jens Erik Fenstad, Raphael Høegh-Krohn, Tom Lindstrøm Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.
Number Systems and the Foundations of Analysis by Elliott Mendelson Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.
