Updated and Revised 2nd edition Topology is an integral part of the undergraduate mathematics curriculum. It wisely restricts itself to point-set topology which it develops axiomatically; experience has shown that a rigorous treatment of combinatorial topology is best left for graduate study after the student has acquired the necessary algebraic background. A sufficient amount of abstract set theory is presented to enable to present in succession metric spaces, topological spaces, compactness, separation, connectedness, and approximation (a good treatment of the Stone-Weierstrass theorem appears here). The stage is now set to present some of the topics in analysis which are currently of central interest; this occupies the second part of the book where, following a preliminary chapter on algebraic systems, the author proceeds to deal with Branch spaces, Hilbert spaces, and Banach algebras. The textbook is eminently readable, uses present-day commonly accepted notation and terminology, and is well documented with good illustrative examples and exercises. A good undergraduate course in classical analysis should serve as an adequate prerequisite for its study. The first part of the book could then constitute a one-semester course in topology; the second part of the book could serve as an excellent introduction to modern analysis followed by a new section
