Rings of Continuous Functions

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  • Format: Paperback
  • Copyright: 2018-01-16
  • Publisher: Dover Publications

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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.

Author Biography

American mathematician Meyer Jerison (1922–1995) was on the faculty of Purdue University from 1951 until his retirement in 1991.
Leonard E. Gilman (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.

Table of Contents

1. Functions on a Topological Space
2. Ideals and Z-Filters
3. Completely Regular Spaces
4. Fixed Ideals. Compact Spaces
5. Ordered Residue Class Rings
6. The Stone-Cech Compactification
7. Characterization of Maximal Ideals
8. Reralcompact Spaces
9. Cardinals of Closed cSets in BX
10. Homomorphisims and Continuos Mappings
11. Embedding in Products of Real Lines
12. Discrete Spaces. Nonmeasurable Cardinals
13. Hyper-Real Residue Class Fields
14. Prime Ideals
15. Uniform Spaces
16. Dimension
List of Symbols

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