Real Analysis through Modern InfinitesimalsCambridge University Press, 17 בפבר׳ 2011 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. |
תוכן
Part I Elements of real analysis | 15 |
Part II Elements of abstract analysis | 331 |
Vector spaces | 521 |
The badic representationof numbers | 523 |
Finite denumerableand uncountable sets | 536 |
The syntax ofmathematical languages | 544 |
References | 554 |
| 557 | |
מהדורות אחרות - הצג הכל
Real Analysis Through Modern Infinitesimals <span dir=ltr>Nader Vakil</span> תצוגה מקדימה מוגבלת - 2011 |
מונחים וביטויים נפוצים
analysis apply Banach space basis bounded called Cauchy closed compact complete condition consider contains contradiction converges Corollary defined Definition denoted derivative differentiable discussed element equal equation equicontinuous equivalent example Exercise exists extended external finite formula function function f given Hausdorff Hence holds hypothesis implies induction inequality infinite integral interval let f limit locally mathematical mean mean value theorem metric space monotone n e Z+ nonempty normed notation Note Proof Proof Assume properties Prove provides reader real number Recall relation Remark result Riemann Riemann integrable satisfies sequence standard statement subset Suppose symbols Theorem Let theory topological space topology transfer axiom uniform unique unlimited vector space write