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[ 洋図書 ] Real analysis through modern infinitesimals / ( Encyclopedia of mathematics and its applications ; 140 )

Nader Vakil. -- Cambridge University Press, -- 2011. --

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ISBN 1107002028 (hardback)
ISBN13桁 9781107002029 (hardback)
テキストの言語 英語                  
分類：NDC10版 410.8
個人著者標目 Vakil, Nader,
生没年等 1948-
本タイトル Real analysis through modern infinitesimals /
著者名 Nader Vakil.
出版地・頒布地 Cambridge ;
出版者・頒布者名 Cambridge University Press,
出版年・頒布年 2011.
数量 xix, 565 p. ;
大きさ 24 cm.
書誌注記 Includes bibliographical references (p. [554]-556) and index.
内容注記 Machine generated contents note: Preface; Introduction; Part I. Elements of Real Analysis: 1. Internal set theory; 2. The real number system; 3. Sequences and series; 4. The topology of R; 5. Limits and continuity; 6. Differentiation; 7. Integration; 8. Sequences and series of functions; 9. Infinite series; Part II. Elements of Abstract Analysis: 10. Point set topology; 11. Metric spaces; 12. Complete metric spaces; 13. Some applications of completeness; 14. Linear operators; 15. Differential calculus on Rn; 16. Function space topologies; A. Vector spaces; B. The b-adic representation of numbers; C. Finite, denumerable, and uncountable sets; D. The syntax of mathematical languages; References; Index.
要約、抄録、注釈等 "Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, self-study, and as a source for advanced undergraduate or graduate courses"--,"This book provides a course in mathematical analysis using the methods of modern infinitesimals, which are developed within the framework of internal set theory (IST), introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the author provides a careful development of the theory in which each external class is represented as a proper class. The basic standard and nonstandard properties of the real numbers follow, together with a thorough discussion of the central topics of analysis that begins with those usually discussed in an advanced undergraduate course and gradually moves to topics suitable for more advanced readers"--
シリーズ名・巻次 Encyclopedia of mathematics and its applications ; 140
一般件名 Mathematical analysis.
Set theory.
資料情報1 『Real analysis through modern infinitesimals /』（Encyclopedia of mathematics and its applications ; 140）　Nader Vakil.　Cambridge University Press,　2011. （所蔵館：中央　 請求記号：F/410.8/E56/E1-140　 資料コード：5020254930）
URL https://catalog.library.metro.tokyo.lg.jp/winj/opac/switch-detail.do?lang=ja&bibid=1348370832

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