Ebook: Nonstandard Methods of Analysis
- Tags: Mathematical Logic and Foundations, Real Functions, Functional Analysis, Topology, Optimization
- Series: Mathematics and Its Applications 291
- Year: 1994
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
Nonstandard Methods of Analysis is concerned with the main trends in this field; infinitesimal analysis and Boolean-valued analysis. The methods that have been developed in the last twenty-five years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Boolean-valued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years.
For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work.
Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-2
Excursus into the History of Mathematical Analysis....Pages 3-12
Naive Fundamentals of Infinitesimal Methods....Pages 13-40
Set-Theoretic Formalisms of Nonstandard Analysis....Pages 41-80
Monads in General Topology....Pages 81-111
Infinitesimals and Subdifferentials....Pages 112-168
Front Matter....Pages 169-171
Universes of Sets....Pages 171-213
Boolean-Valued Universes....Pages 214-262
Functors of Boolean-Valued Analysis....Pages 263-323
Boolean-Valued Analysis of Algebraic Systems....Pages 324-376
Boolean Representations in Functional Analysis....Pages 377-403
Back Matter....Pages 404-439
Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-2
Excursus into the History of Mathematical Analysis....Pages 3-12
Naive Fundamentals of Infinitesimal Methods....Pages 13-40
Set-Theoretic Formalisms of Nonstandard Analysis....Pages 41-80
Monads in General Topology....Pages 81-111
Infinitesimals and Subdifferentials....Pages 112-168
Front Matter....Pages 169-171
Universes of Sets....Pages 171-213
Boolean-Valued Universes....Pages 214-262
Functors of Boolean-Valued Analysis....Pages 263-323
Boolean-Valued Analysis of Algebraic Systems....Pages 324-376
Boolean Representations in Functional Analysis....Pages 377-403
Back Matter....Pages 404-439
....