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Rings of Continuous Function : Lecture Notes in Pure and Applied Mathematics - C. E. Aull

Rings of Continuous Function

Lecture Notes in Pure and Applied Mathematics

Paperback Published: 1st March 1985
ISBN: 9780824771447
Number Of Pages: 318

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This timely work is the first book in several years to review and update important developments in the study of rings of continuous functions. Integrating the recent efforts of leading mathematicians, Rings of Continuous Functions presents chapters with varying emphasis on algebra, analysis, and general topology with particular focus on category theory, cardinality axioms, and set theory. Additionally, historical perspectives and a review of early contributions by leading Soviet mathematicians such as P. S. Aleksandrov and A. N. Tychonov help provide a full, up-to-date understanding of current knowledge. An unparalleled overview of the state of the art, Rings of Continuous Functions will be an invaluable reference for topologists, algebraists, analysts, and geometers active in the field, and an excellent introduction for interested nonspecialist mathematicians. Also, research problems raised in each chapter and in a special final chapter offer provocative avenues for further research -- facilitated by more than 300 literature citations. Book jacket.

Prefacep. iii
Contributorsp. ix
Some Genealogies in Rings of Continuous Functionsp. 1
A Cardinal Generalization of z-Embeddingp. 7
The Birth of the Stone-Cech Compactificationp. 67
Generalized Perfect Maps and a Theorem of I. Juhaszp. 79
On Initially [kappa]-Compact Spacesp. 103
Relatively Uniformly Complete [Phi]-Algebrasp. 109
Extreme Positive Operators and Function Spacesp. 125
A Note on Extending Zero Sets from the Real Linep. 141
Rings of Continuous Functions Are Rings: A Surveyp. 143
C(X) Has No Proper Functorial Hullsp. 149
Algebraic Closures of l-Groups of Continuous Functionsp. 165
Unsolved Problems on Algebraic Aspects of C(X)p. 195
Prime Ideals in Function Ringsp. 203
Partial Extension of Bounded Functions to Compactificationsp. 207
The Extension of Uniformly Continuous Banach Space-Valued Mappingsp. 219
The Long Line as a Remainderp. 237
N-Compactness, Metrizability, and Covering Dimensionp. 247
Concerning the Equation C([Pi]{X[subscript a]}/sb) = C(&Pi{wX[subscript a]})p. 277
Some Topological Characterizations of the Generalized Continuum Hypothesisp. 283
More Realcompact Spacesp. 289
Hausdorff Extension Properties: A Summaryp. 301
Problem Sectionp. 311
Indexp. 315
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780824771447
ISBN-10: 0824771443
Series: Lecture Notes in Pure and Applied Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 318
Published: 1st March 1985
Publisher: TAYLOR & FRANCIS
Country of Publication: US
Dimensions (cm): 25.04 x 17.68  x 1.65
Weight (kg): 0.59
Edition Number: 1

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