<電子ブック>
Rings of Continuous Functions / by L. Gillman, M. Jerison
(The university series in higher mathematics)
版 | 1st ed. 1960. |
---|---|
出版者 | New York, NY : Springer New York : Imprint: Springer |
出版年 | 1960 |
本文言語 | 英語 |
大きさ | IX, 300 p : online resource |
著者標目 | *Gillman, L author Jerison, M author SpringerLink (Online service) |
件 名 | LCSH:Medical sciences FREE:Health Sciences |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-1-4615-7819-2 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9781461578192 |
|
電子リソース |
|
EB00227712 |
類似資料
この資料の利用統計
このページへのアクセス回数:10回
※2017年9月4日以降