A Guide to Topologyby Steven G. Krantz
Pub. Date: 08/03/2009
Publisher: Mathematical Association of America
A Guide to Topology is an introduction to basic topology for graduate or advanced undergraduate students. It covers point-set topology, Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations. Students studying for exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too.
- Mathematical Association of America
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- 6.10(w) x 9.10(h) x 0.50(d)
Table of ContentsPreface; Part I. Fundamentals: 1.1. What is topology?; 1.2. First definitions; 1.3 Mappings; 1.4. The separation axioms; 1.5. Compactness; 1.6. Homeomorphisms; 1.7. Connectedness; 1.8. Path-connectedness; 1.9. Continua; 1.10. Totally disconnected spaces; 1.11. The Cantor set; 1.12. Metric spaces; 1.13. Metrizability; 1.14. Baire's theorem; 1.15. Lebesgue's lemma and Lebesgue numbers; Part II. Advanced Properties: 2.1 Basis and subbasis; 2.2. Product spaces; 2.3. Relative topology; 2.4. First countable and second countable; 2.5. Compactifications; 2.6. Quotient topologies; 2.7. Uniformities; 2.8. Morse theory; 2.9. Proper mappings; 2.10. Paracompactness; Part III. Moore-Smith Convergence and Nets: 3.1. Introductory remarks; 3.2. Nets; Part IV. Function Spaces: 4.1. Preliminary ideas; 4.2. The topology of pointwise convergence; 4.3. The compact-open topology; 4.4. Uniform convergence; 4.5. Equicontinuity and the Ascoli-Arzela theorem; 4.6. The Weierstrass approximation theorem; Table of notation; Glossary; Bibliography; Index.
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