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

Gillman, L.; Jerison, M.

ISBN 10: 0387901981 / ISBN 13: 9780387901985

Verlag: Springer, 1976

Beschreibung

Unmarked hardcover in no jacket.

Bestandsnummer des Verkäufers 147807

Bibliografische Details

• Titel: Rings of Continuous Functions (The university series in higher mathematics)
• Verlag: Springer
• Erscheinungsjahr: 1976
• Sprache: Englisch
• ISBN-10: 0387901981
• ISBN-13: 9780387901985
• Einband: hardcover
• Auflage: 1st ed. 1960. 2nd printing 1976.
• Zustand: Good
• Gewicht: 22 Unzen
• Verkäuferkataloge:
  • MATHEMATICS

Über diesen Titel

Inhaltsangabe

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.