Counterexamples in Analysis
These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.
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While most mathematical textbooks are devoted to the proof of true statements, this text focuses on counterexamples for proving statements are false. The 13 chapters cover differentiation, Riemann integration, sequences, infinite series, sets of real numbers, functions of two variables, and metric and topological spaces. Originally published by Holden-Day in 1964. Annotation ©2003 Book News, Inc., Portland, OR
Part I.Functions of a Real Variable1.The Real Number System2.Functions and Limits3.Differentiation4.Riemann Integration5.Sequences6.Infinite Series7.Uniform Convergence8.Sets and Measure on the Real AxisPart II.Higher Dimensions9.Functions of Two Variables10.Plane Sets11.Area12.Metric and Topological Spaces13.Function SpacesBibliography180Special Symbols183Index187Errata195
