Introductory Problem Courses in Analysis and Topology (Universitext) - Softcover

Moise, E.E.

Softcover

ISBN 10: 0387907017 ISBN 13: 9780387907017

Verlag: Springer, 2013

Inhaltsangabe

Analysis.- 1. Notations.- 2. The Real Numbers, Regarded as an Ordered Field.- 3. Functions, Limits, and Continuity.- 4. Integers. Sequences. The Induction Principle.- 5. The Continuity of ?.- 6. The Riemann Integral of a Bounded Function.- 7. Necessary and Sufficent Conditions for Integrability.- 8. Invertible Functions. Arc-length and Path-length.- 9. Point-wise Convergence and Uniform Convergence.- 10. Infinite Series.- 11. Absolute Convergence. Rearrangements of Series.- 12. Power Series.- 13. Power Series for Elementary Functions.- Topology.- 1. Sets and Functions.- 2. Metric Spaces.- 3. Neighborhood Spaces and Topological Spaces.- 4. Cardinality.- 5. The Completeness of ?. Uncountable Sets.- 6. The Schröder-Bernstein Theorem.- 7. Compactness in ?n.- 8. Compactness in Abstract Spaces.- 9. The Use of Choice in Existence Proofs.- 10. Linearly Ordered Spaces.- 11. Mappings Between Metric Spaces.- 12. Mappings Between Topological Spaces.- 13. Connectivity.- 14. Well-ordering.- 15. The Existence of Well-orderings. Zorn's Lemma.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 0387907017
• ISBN 13: 9780387907017
• Einband: Taschenbuch
• Anzahl der Seiten: 108
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