Boolean Valued Analysis

ISBN-13: 9780792359210 / Angielski / Twarda / 1999 / 336 str.

A. G. Kusraev; S. S. Kutateladze; Anatoly G. Kusraev

Opis

Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe.

Spis treści

Foreword to the English Translation. Preface. 1. Universes of Sets. 2. Boolean Valued Universes. 3. Functors of Boolean Valued Analysis. 4. Boolean Valued Analysis of Algebraic Systems. 5. Boolean Valued Analysis of Banach Spaces. 6. Boolean Valued Analysis of Banach Algebras. Appendix. References. Subject Index.