Rajwade A.R., Bhandari A.K. Surprises and Counterexamples in Real Function Theory

New Delhi: Hindustan Book Agency, 2007. — 302 p.Our aim in this book is to consider a variety of intriguing, surprising and appealing topics, and nonroutine proofs of the usual results of real function theory. The reader is expected to have done a first course in real analysis (or advanced calculus), since the book assumes a knowledge of continuity and differentiability of functions, Rolle's theorem, the mean value theorem, Taylor expansion and Riemann integration. However, no sophisticated knowledge of analysis is required and a student at the masters or advanced undergraduate level should have no difficulty in going through the book.
Though this book has some part of the title common with the book "Coun- terexamples in Analysis" by Gelbaum and Olmstead, it is totally different in nature and contents. Some examples and counterexamples (fifteen or twenty) in our book are essentially the same as given in the book by Gelbaum and Olmstead, but otherwise the intersection is small.