Rings of Continuous Functions (The university series in higher mathematics)

Gillman, L.; Jerison, M.

ISBN 10: 0387901981 / ISBN 13: 9780387901985

Editore: Springer, 1976

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Unmarked hardcover in no jacket.

Codice articolo 147807

Dati bibliografici

• Titolo: Rings of Continuous Functions (The university series in higher mathematics)
• Editore: Springer
• Data di pubblicazione: 1976
• Lingua: Inglese
• ISBN 10: 0387901981
• ISBN 13: 9780387901985
• Rilegatura: hardcover
• Edizione: 1st ed. 1960. 2nd printing 1976.
• Condizione: Good
• Peso: 22 once
• Cataloghi dei venditori:
  • MATHEMATICS

Descrizione articolo

Riassunto

This book is addressed to those who know the meaning of each word in the title: none is defined in the text. The reader can estimate the knowledge required by looking at Chapter 0; he should not be dis­ couraged, however, if he finds some of its material unfamiliar or the presentation rather hurried. Our objective is a systematic study of the ring C(X) of all real-valued continuous functions on an arbitrary topological space X. We are con­ cerned with algebraic properties of C(X) and its subring C*(X) of bounded functions and with the interplay between these properties and the topology of the space X on which the functions are defined. Major emphasis is placed on the study of ideals, especially maximal ideals, and on their associated residue class rings. Problems of extending continuous functions from a subspace to the entire space arise as a necessary adjunct to this study and are dealt with in considerable detail. The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5 and the beginning of Chapter 10, presents the fundamental aspects of the subject insofar as they can be discussed without introducing the Stone-Cech compactification. In Chapter 3, the study is reduced to the case of completely regular spaces.

Contenuti

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-?ech Compactification.- 7 Characterization of Maximal Ideals.- 8 Realcompact Spaces.- 9 Cardinals of Closed Sets in ?X.- 10 Homomorphisms and Continuous 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.- Notes.- List of Symbols.