Rings of continuous functions /
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| Author / Creator: | Gillman, Leonard |
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| Imprint: | New York : Springer-Verlag, 1976, c1960. |
| Description: | xiii, 300 p. ; 25 cm. |
| Language: | English |
| Series: | Graduate texts in mathematics 43 Graduate texts in mathematics 43 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/300534 |
| Summary: | 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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| Item Description: | Reprint of the 1960 ed. published by Van Nostrand, Princeton, N.J., in series: The University series in higher mathematics. Includes index. |
| Physical Description: | xiii, 300 p. ; 25 cm. |
| Bibliography: | Bibliography: p. 278-283. |
| ISBN: | 0387901981 |