Nonstandard Methods of AnalysisNonstandard 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. |
Contents
Settheoretic formalisms of nonstandard analysis | 41 |
vi | 65 |
Monads in general topology | 81 |
Copyright | |
9 other sections not shown
Other editions - View all
Nonstandard Methods of Analysis A. G. Kusraev,Semën Samsonovich Kutateladze No preview available - 2014 |
Nonstandard Methods of Analysis A.G. Kusraev,Semën Samsonovich Kutateladze No preview available - 2012 |
Common terms and phrases
algebraic system arbitrary axiom B-set B-system Boolean-valued models calculus Cauchy filter complete Boolean algebra cones correspondence deduce definition denoted descent Edom Edom(x EV(B extensional external sets Eµ(F filter F finite following statements formula function functor Hence homomorphism idealization principle implies infinitely close infinitely large infinitely small infinitesimal inside V(B internal set isomorphism K-space Let us assume Let us choose Let us consider mapping mathematical monad natural numbers nearstandard neighbourhood Neumann universe nonstandard analysis Obviously operations ordinal partition of unity predicate prenearstandard prove real numbers relation remarked ring set theory set-theoretic signature standard element standard set statements are equivalent statements are valid subset symbol theorem topological space topology totally bounded transfer principle uniform space vector lattice vector space virtue von Neumann universe zero