Sets, sequences and mappings : the basic concepts of analysis / Kenneth W. Anderson, Dick Wick Hall.

Originally published: New York : Wiley, 1963.

Includes index.

DOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; Preface; Table of Contents; I -- Introduction to sets and mappings; 1. Sets; 2. Mappings; 3. Real numbers; 4. Suprema and infima; II -- Sequences; 1. Monotone and bounded sequences; 2. Uniformly isolated sequences; III -- Countable, connected, open, and closed sets; 1. Countable sets; 2. Connected sets. Open intervals and open rays; 3. Open sets and components; 4. Closed sets. Compact sets; IV -- Convergence; 1. Convergent sequences; 2. Properties of limits; 3. Cauchy sequences; 4. Neighborhoods, cluster points, and sequential compactness.

V -- Continuity and uniform continuity1. Continuous functions; 2. Other criteria for continuity; 3. Uniform continuity and extension theorems; 4. An application of continuous mappings; VI -- Metric spaces; 1. Cartesian products, metrics, and metric sets; 2. Open and closed sets. Metric spaces; 3. Sequentially compact sets in metric spaces; 4. Separability and compactness; Lindelöf and Cantor Product Theorems; 5. Continuity, uniform continuity, and connectedness; Index of Axioms and Key Theorems; Index; A CATALOG OF SELECTED DOVER BOOKS IN SCIENCE AND MATHEMATICS.

Students progressing to advanced calculus are frequently confounded by the dramatic shift from mechanical to theoretical and from concrete to abstract. This text bridges the gap, offering a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. The first five chapters consist of a systematic development of many of the important properties of the real number system, plus detailed treatment of such concepts as mappings, sequences, limits, and continuity. The sixth and final chapter discusses metric spaces and generaliz.