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Counterexamples in Analysis

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Counterexamples in Analysis

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.

Reprint of the Holden-Day, Inc., San Francisco, 1962 edition.
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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.

Reprint of the Holden-Day, Inc., San Francisco, 1962 edition.
algebraic geometry;measure theory;algebraic topology;vector spaces;galois theory;advanced calculus;functional analysis;abstract algebra;self study;advanced material;studying mathematics;chapter talked;category theory;varying difficulty;students preparing;algebra class;level mathematics;linear algebra;advanced undergraduate;field theory;phd student;graduate level;material covered;graduate students;fairly thorough;algebras;polynomials;lemma;topologies;lebesgue;dedekind;hungerford;tensor;axler;counterexamples;nontrivial;steen;counter-examples;topological;compactness;burnside;exteriors;theorems;modules;foote;variables;notation;finite;proofs;lang;probability;mathematician;proposition;mathematical;functions;exercises;study mathematics;books on tensors;books on lemma;books on advanced calculus;books on modules;books on galois theories;books on graduate levels;books on advanced materials;books on field theories;books on linear algebras;books on algebras;books on algebra classes;books on studying mathematics;books on graduate students;books on vector spaces;books on topologies;books on self studies;books on level mathematics;books on phd students;books on lebesgue;books on lang;books on hungerford;books on exteriors;books on polynomials;books on abstract algebras;books on algebraic topologies;books on measure theories;books on dedekinds;books on algebraic geometries;books on steen;books on advanced undergraduates;books on category theories;books on axler;books on functional analysis
Counterexamples in Analysis | Dover Publications