Homeomorphisms in Analysis by Casper Goffman
Homeomorphisms in Analysis - Table of Contents
- Part 1. The One Dimensional Case
- 1. Subsets of R
- 2. Baire Class 1
- 3. Differentiability Classes
- 4. The Derivative Function
- Part 2. Mappings and Measures on R^n
- 5. Bi-Lipschitzian Homeomorphisms
- 6. Approximation by Homeomorphisms
- 7. Measures on R^n
- 8. Blumberg's Theorem
- Part 3. Fourier Series
- 9. Behavior of Fourier Series
- 10. Preservation of Convergence
- 11. Fourier Series of Integrable Functions
- Appendix: Supplementary Material
- A.1. Baire, Borel and Lebesgue
- A.2. Lipschitzian Functions
- A.3. Bounded Variation
- A.4. Density Topology
- A.5. Approximately Continuous Maps
- A.6. Hausdorff Dimension
- A.7. Hausdorff Packing
- A.8. Non Parametric Length
- A.9. Schwarz's Example
- A.10. Lebesgue's Lower Semicontinuous Area
- A.11. Distribution Derivatives
What You Will Learn in Homeomorphisms in Analysis
Homeomorphisms in Analysis by Casper Goffman is an advanced, highly specialized text designed for graduate students and researchers in mathematical analysis, topology, and measure theory. The book bridges classical real variable theory with modern geometric analysis, covering core analytical topics across its primary parts and comprehensive appendices: Subsets of R, Baire Class 1, and Differentiability Classes, Mappings, Bi-Lipschitzian Homeomorphisms, and Measures on R^n, Fourier Series Behavior and Convergence Preservation, and specialized appendices covering Baire/Borel/Lebesgue sets, Approximate Continuity, Hausdorff Measure, and Non-Parametric Area.
This book serves as an invaluable guide for graduate students and professional mathematicians who want to build a deep, rigorous understanding of how topological homeomorphisms interact with differential properties and measure spaces. Goffman combines rigorous theoretical developments with subtle counterexamples, ensuring readers develop advanced analytical reasoning skills.
Due to its unique focus and authoritative presentation, it is widely recognized as an outstanding reference text for advanced real analysis and geometric measure theory. Rather than restricting itself to elementary functions, it equips learners with the advanced mapping tools necessary for modern topological dynamics, real analysis research, and geometric topology.
Book Details & Specifications
Title:
Homeomorphisms in Analysis by Casper Goffman
Publisher:
American Mathematical Society
Year:
1997
Pages:
216
Type:
PDF
Language:
English
ISBN-10 #:
0821806149
ISBN-13 #:
9780821806142
License:
External Educational Resource
Amazon:
Amazon
About the Author: Casper Goffman
The author Casper Goffman
was a prominent American mathematician and professor renowned for his influential research in real analysis, measure theory, topology, and geometric integration.
Through Homeomorphisms in Analysis, Goffman successfully synthesized complex mapping properties and analytical structures into a clear, rigorous monograph. His expert mathematical exposition makes this text a masterpiece resource for advanced real and harmonic analysis.
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