Introductory Problem Courses in Analysis and Topology

AvE.E. Moise

Häftad, Engelska, 1982

Del i serien Universitext

556 kr

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E-bok

718 kr

Produktinformation

Utgivningsdatum:1982-05-05
Mått:155 x 235 x 7 mm
Vikt:178 g
Format:Häftad
Språk:Engelska
Serie:Universitext
Antal sidor:94
Förlag:Springer-Verlag New York Inc.
ISBN:9780387907017

Utforska kategorier

Innehållsförteckning

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.

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