Rings of Continuous Functions - Brossura

Gillman, L.; Jerison, M.

Brossura

ISBN 10: 1461578205 ISBN 13: 9781461578208

Casa editrice: Springer, 2013

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.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2013
• ISBN 10: 1461578205
• ISBN 13: 9781461578208
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 312
• Contatto del produttore: non disponibile