Vicente Montesinos

Petr Habala

Petr Hájek

Marián Fabian

Václav Zizler

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

The Basis for Linear and Nonlinear Analysis

Banach Space Theory

The proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Gödel's birth. The papers in this volume cover the wide range of topics Gödel's work touched, and affirm its continuing importance.

Gödel '96

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named `fuzzy inference' can be naturally understood as logical deduction. There are two main groups of intended readers. First, logicians: they can see that fuzzy logic is indeed a branch of logic and may find several very interesting open problems. Second, equally important, researchers involved in fuzzy logic applications and soft computing. As a matter of fact, most of these are not professional logicians so that it can easily happen that an application, clever and successful as it may be, is presented in a way which is logically not entirely correct or may appear simple-minded. (Standard presentations of the logical aspects of fuzzy controllers are the most typical example.) This fact would not be very important if only the bon ton of logicians were harmed; but it is the opinion of the author (who is a mathematical logician) that a better understanding of the strictly logical basis of fuzzy logic (in the usual broad sense) is very useful for fuzzy logic appliers since if they know better what they are doing, they may hope to do it better. In addition, a better mutual understanding between (classical) logicians and researchers in fuzzy logic, promises to lead to deeper cooperation and new results.

Metamathematics of Fuzzy Logic

Hrdinou společenského románu ze současného pražského prostředí je mladý muž, který v dramatických chvílích života, kdy je podezříván ze zločinu, pozitivně řeší vztah k ženě, rodině a společnosti. Myšlenkovým jádrem prózy jsou.

Petr Hájek

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