Liebe Besucherinnen und Besucher,
heute ab 15 Uhr feiern wir unser Sommerfest und sind daher nicht erreichbar. Ab morgen sind wir wieder wie gewohnt für Sie da. Wir bitten um Ihr Verständnis – Ihr Team von Sack Fachmedien
Chapters 1-4
Buch, Englisch, 437 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 674 g
ISBN: 978-3-540-64241-1
Verlag: Springer Berlin Heidelberg
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
of the Elements of Mathematics Series.- I. Topological Structures.- § 1. Open sets, neighbourhoods, closed sets.- § 2. Continuous functions.- § 3. Subspaces, quotient spaces.- § 4. Product of topological spaces.- § 5. Open mappings and closed mappings.- § 6. Filters.- § 7. Limits.- § 8. Hausdorff spaces and regular spaces.- § 9. Compact spaces and locally compact spaces.- § 10. Proper mappings.- §11. Connectedness.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Exercises for § 5.- Exercises for § 6.- Exercises for § 7.- Exercises for § 8.- Exercises for § 9.- Exercises for § 10.- Exercises for § 11.- Historical Note.- II. Uniform Structures.- § 1. Uniform spaces.- § 2. Uniformly continuous functions.- § 3. Complete spaces.- § 4. Relations between uniform spaces and compact spaces.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Historical Note.- III: Topological Groups.- § 1. Topologies on groups.- § 2. Subgroups, quotient groups, homomorphisms, homogeneous spaces, product groups.- § 3. Uniform structures on groups.- § 4. Groups operating properly on a topological space; compactness in topological groups and spaces with operators.- § 5. Infinite sums in commutative groups.- § 6. Topological groups with operators; topological rings, division rings and fields.- § 7. Inverse limits of topological groups and rings.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Exercises for § 5.- Exercises for § 6.- Exercises for § 7.- Historical Note.- IV: Real Numbers.- § 1. Definition of real numbers.- § 2. Fundamental topological properties of the real line.- § 3. The field of real numbers.- § 4. The extended real line.- § 5. Real-valued functions.- § 6. Continuous and semi-continuous real-valued functions.- § 7. Infinite sums and products of real numbers.- § 8. Usual expansions of real numbers; the power of R.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Exercises for § 5.- Exercises for § 6.- Exercises for § 7.- Exercises for § 8.- Historical Note.- Index of Notation (Chapters I–IV).- Index of Terminology (Chapters I–IV).