Designed as a text as well as a treatise for active mathematicians, this volume begins with an unusual notice: The book is addressed to those who know the meaning of each word in the title. As such, it constituted the first systematic account of the theory of rings of continuous functions, and it has retained its secure position as the basic graduate-level book in this area.
The authors focus on characterizing the maximal ideals and classifying their residue class fields. Problems concerning extending continuous functions from a subspace to the entire space play a fundamental role in the study, and these problems are discussed in extensive detail. A thorough treatment of the Stone-Čech compactification is supplemented with a number of related topics: the Ulam measure problem, the theory of uniform spaces, and a small but significant portion of dimension theory. Hundreds of problems of varying difficulty appear throughout the text, providing additional details, describing counterexamples, and outlining new topics.
Rings of Continuous Functions
Description
Table of Contents
Foreword1. Functions on a Topological Space2. Ideals and Z-Filters3. Completely Regular Spaces4. Fixed Ideals. Compact Spaces5. Ordered Residue Class Rings6. The Stone-Cech Compactification7. Characterization of Maximal Ideals8. Reralcompact Spaces9. Cardinals of Closed cSets in BX10. Homomorphisims and Continuos Mappings11. Embedding in Products of Real Lines12. Discrete Spaces. Nonmeasurable Cardinals13. Hyper-Real Residue Class Fields14. Prime Ideals15. Uniform Spaces16. DimensionNotesBibliographyList of SymbolsIndex
Author Description
American mathematician Meyer Jerison (1922-1995) was on the faculty of Purdue University from 1951 until his retirement in 1991.
Leonard E. Gillman (1917-2009) taught at the University of Rochester and the University of Texas and was President of the Mathematical Association of America in 1987-1988.