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.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 12 mm
Gewicht
ISBN-13
978-0-88385-346-7 (9780883853467)
Schweitzer Klassifikation
Steven G. Krantz was born in San Francisco, California and grew up in Redwood City, California. He received his undergraduate degree from the University of California at Santa Cruz and the Ph.D. from Princeton University. Krantz has held faculty positions at UCLA, Princeton University, Penn State University, and Washington University in St. Louis. He is currently Deputy Director of the American Institute of Mathematics. He has written 160 scholarly papers, over 50 books and is the holder of the Chauvenet Prize and the Beckenbach Book Award.
Preface
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.
