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OverviewThis is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the later chapters of Bourbaki's Topologie generale. It completes the treatment of general topology begun in Part I (Ch. 1-4, also available in English in softcover). The real numbers having been introduced in Ch. 4, the first chapters of this volume study subgroups and quotients of R (with applications to the 'measurement of magnitudes' and to the log and exp functions), then real vector spaces and projective spaces, then the additive groups Rn (subgroups, quotients, homomorphisms, infinite sums and products). Analogous properties are then studied for complex numbers, in Ch.8. Chapter 9 illustrates the use of real numbers in general topology, studying different important kinds of topological spaces: uniformizable, metric, normal Baire, Polish, Borel spaces.The final chapter deals with the various topologies of function spaces,ending with a section on approximation of functions. Full Product DetailsAuthor: N. BourbakiPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1st ed. 1989, 2nd printing 1998 Volume: 16 Dimensions: Width: 15.50cm , Height: 1.90cm , Length: 23.50cm Weight: 0.668kg ISBN: 9783540645634ISBN 10: 3540645632 Pages: 363 Publication Date: 03 August 1998 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsV: One-parameter groups.- § 1. Subgroups and quotient groups of R.- § 2. Measurement of magnitudes.- § 3. Topological characterization of the groups R and T.- § 4. Exponentials and logarithms.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Historical Note.- VI. Real number spaces and projective spaces.- § 1. Real number space Rn.- § 2. Euclidean distance, balls and spheres.- § 3. Real projective spaces.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Historical Note.- VII. The additive groupsRn.- § 1. Subgroups and quotient groups of Rn.- § 2. Continuous homomorphisms of Rn and its quotient groups.- § 3. Infinite sums in the groups Rn.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Historical Note.- VIII. Complex numbers.- § 1. Complex numbers, quaternions.- § 2. Angular measure, trigonometric functions.- § 3. Infinite sums and products of complex numbers.- § 4. Complex number spaces and projective spaces.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Historical Note.- IX. Use of real numbers in general topology.- § 1. Generation of a uniformity by a family of pseudometrics; uniformizable spaces.- § 2. Metric spaces and metrizable spaces.- § 3. Metrizable groups, valued fields, normed spaces and algebras.- § 4. Normal spaces.- § 5. Baire spaces.- § 6. Polish spaces, Souslin spaces, Borel sets.- Appendix: Infinite products in normed algebras.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Exercises for § 5.- Exercises for § 6.- Exercises for the Appendix.- Historical Note.- X. Function spaces.- §1. The uniformity of 𝔖-convergence.- § 2. Equicontinuous sets.- § 3. Special function spaces.- § 4. Approximation of continuous real-valued functions.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Historical Note.- Index of Notation.- Index of Terminology.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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