Introductory Problem Courses in Analysis and Topology

Softcover Nachdruck of the original 1. Auflage 1982
ISBN: 978-0-387-90701-7
Verlag: Springer

Buch, Englisch, 94 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 178 g

Reihe: Universitext

Springer Book Archives

Zielgruppe

Research

Autoren/Hrsg.

Moise, E. E.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

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.