Counterexamples in Analysis

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Dover Publications, 04 giu 2003 - 195 pagine
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These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students. 12 figures. Bibliography. Index. Errata.

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Review: Counterexamples in Analysis

Recensione dell'utente  - Goodreads

Although it does give some rather arcane examples where a detailed abstract description would have sufficed, it does give a concise collection of concrete counterexamples, some of which may have slipped under your radar. Leggi recensione completa

Review: Counterexamples in Analysis

Recensione dell'utente  - Goodreads

The book contains some important examples, but most of them are too arcane and inelegant. Leggi recensione completa

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Informazioni sull'autore (2003)

BERNARD R. GELBAUM is Professor of Mathematics at the State University of New York at Buffalo. He has previously served on the faculties of the University of Minnesota, the University of California, Irvine, and as a Fulbright Senior Scholar at University College, Galway, Ireland. He has published research in analysis and probability theory and is the author of Theorems and Counterexamples in Mathematics; Problems in Real and Complex Analysis; and Linear Algebra: Basics, Practice and Theory.

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