Rings of Continuous Functions: 43 (The university series in higher mathematics)

Gillman, L.; Jerison, M.

ISBN 10: 0387901981 ISBN 13: 9780387901985

Verlag: Springer, 1976

Sprache: Englisch

Zustand: Good Hardcover

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Slight tanning to pages. Fading to boards and spine. Boards a little marked.

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Bibliografische Details

Titel

Rings of Continuous Functions: 43 (The university series in higher mathematics)

Verlag

Springer

Ver�ffentlichungsdatum

1976

Sprache

Englisch

ISBN-10

0387901981

ISBN-13

9780387901985

Bindung

hardcover

Ausgabe

1st ed. 1960. 2nd printing 1976.

Zustand

Good

Zustand des Schutzumschlags

No D/J as Published

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MATHEMATICS

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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.

Rese�a del editor

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.

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