Download or read book Monografie Matematyczne written by and published by . This book was released on 1969 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Glasnik Matematicki written by and published by . This book was released on 1981 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Andrzej Mostowski and Foundational Studies written by A. Ehrenfeucht and published by IOS Press. This book was released on 2008-03-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andrzej Mostowski was one of the leading 20th century logicians. His legacy is examined in this volume of papers devoted both to his extraordinary scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and human. Professor Mostowski pioneered and mastered many areas of mathematical logic. His contributions spanned set theory, recursion theory, and model theory - the backbone of foundations of mathematics. He is best known of the Kleene-Mostowski and Davis-Mostowski hierarchies of properties of integers reflecting the complexity of their definitions, and of the very elegant concept of a generalized quantifier which inspired and keeps stimulating a stream of deep work on fundamental issues of logics, deduction and reasoning both in mathematics and in computer science, and also of the contributions and excellent lectures on undecidability, unprovability, consistency and independence of various statements in set theory and arithmetic following Gödel, Tarski and Cohen. The overall content of the volume is designed to cover the current main streams in the field. For many years after WWII, especially in the late sixties, till his untimely death in 1975, Warsaw - where he led the centre of foundational studies - was a place where many leading logicians visited, studied, and started their career. Their memories form an important part of this volume, attempting to bring back the extraordinary achievements and personality of Mostowski.
Download or read book The Infinite Dimensional Topology of Function Spaces written by J. van Mill and published by Elsevier. This book was released on 2002-05-24 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we study function spaces of low Borel complexity.Techniques from general topology, infinite-dimensional topology, functional analysis and descriptive set theoryare primarily used for the study of these spaces. The mix ofmethods from several disciplines makes the subjectparticularly interesting. Among other things, a complete and self-contained proof of the Dobrowolski-Marciszewski-Mogilski Theorem that all function spaces of low Borel complexity are topologically homeomorphic, is presented. In order to understand what is going on, a solid background ininfinite-dimensional topology is needed. And for that a fair amount of knowledge of dimension theory as well as ANR theory is needed. The necessary material was partially covered in our previous book `Infinite-dimensional topology, prerequisites and introduction'. A selection of what was done there can be found here as well, but completely revised and at many places expanded with recent results. A `scenic' route has been chosen towards theDobrowolski-Marciszewski-Mogilski Theorem, linking theresults needed for its proof to interesting recent research developments in dimension theory and infinite-dimensional topology. The first five chapters of this book are intended as a text forgraduate courses in topology. For a course in dimension theory, Chapters 2 and 3 and part of Chapter 1 should be covered. For a course in infinite-dimensional topology, Chapters 1, 4 and 5. In Chapter 6, which deals with function spaces, recent research results are discussed. It could also be used for a graduate course in topology but its flavor is more that of a research monograph than of a textbook; it is thereforemore suitable as a text for a research seminar. The bookconsequently has the character of both textbook and a research monograph. In Chapters 1 through 5, unless statedotherwise, all spaces under discussion are separable andmetrizable. In Chapter 6 results for more general classes of spaces are presented. In Appendix A for easy reference and some basic facts that are important in the book have been collected. The book is not intended as a basis for a course in topology; its purpose is to collect knowledge about general topology. The exercises in the book serve three purposes: 1) to test the reader's understanding of the material 2) to supply proofs of statements that are used in the text, but are not proven there3) to provide additional information not covered by the text.Solutions to selected exercises have been included in Appendix B.These exercises are important or difficult.
Download or read book Cech and Steenrod Homotopy Theories with Applications to Geometric Topology written by D. A. Edwards and published by Springer. This book was released on 2006-11-14 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integration and Modern Analysis written by John J. Benedetto and published by Springer Science & Business Media. This book was released on 2010-01-08 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.
Download or read book Modern Mathematics written by Facts On File, Incorporated and published by Infobase Publishing. This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: During the first half of the 20th century, mathematics became an international discipline that led to major advances in science and technology. Modern Mathematics: 1900 to 1950 provides an eye-opening introduction to those five historic decades by analyzing the advancement of the field through the accomplishments of 10 significant mathematicians. From David Hilbert and Emmy Noether, who introduced the infinite dimensional vector spaces and algebraic rings that bear their names, to Norbert Wiener, the founder of cybernetics, this in-depth volume is an excellent choice for libraries aiming to provide a range of resources covering the history of mathematics.
Download or read book Fundamentals of Functions and Measure Theory written by Valeriy K. Zakharov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals
Download or read book Hybrid Systems V written by Panos J. Antsaklis and published by Springer. This book was released on 2003-07-31 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the strictly refereed post-proceedings of the 5th International Hybrid Systems Workshop held in Notre Dame, Indiana, USA in September 1998. The 23 revised full papers presented in the book have gone through two rounds of thorough reviewing and revision. The volume presents state-of-the-art research results and particularly addresses such areas as program verification, concurrent and distributed processes, logic programming, logics of programs, discrete event simulation, calculus of variations, optimization, differential geometry, Lie algebras, automata theory, dynamical systems, etc.
Download or read book Functional Analysis and Control Theory written by S. Rolewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Download or read book Ten Papers on Differential Equations and Functional Analysis written by and published by American Mathematical Soc.. This book was released on 1968-12-31 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Framing Global Mathematics written by Norbert Schappacher and published by Springer Nature. This book was released on 2022-06-15 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows the sinuous path that was taken to reach this state, from the long nineteenth century, through the two wars, to the present day. International cooperation in mathematics was well established by 1900, centered in Europe. The first International Mathematical Union, IMU, founded in 1920 and disbanded in 1932, reflected above all the trauma of WW I. Since 1950 the current IMU has played an increasing role in defining mathematical excellence, as is shown both in the historical narrative and by analyzing data about the International Congresses of Mathematicians. For each of the three periods discussed, interactions are explored between world politics, the advancement of scientific infrastructures, and the inner evolution of mathematics. Readers will thus take a new look at the place of mathematics in world culture, and how international organizations can make a difference. Aimed at mathematicians, historians of science, scientists, and the scientifically inclined general public, the book will be valuable to anyone interested in the history of science on an international level.
Download or read book Georg Cantor written by Joseph Warren Dauben and published by Princeton University Press. This book was released on 2020-06-16 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.
Download or read book Banach Function Algebras Arens Regularity and BSE Norms written by Harold Garth Dales and published by Springer Nature. This book was released on with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperspaces written by Alejandro Illanes and published by CRC Press. This book was released on 1999-01-04 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents hyperspace fundamentals, offering a basic overview and a foundation for further study. Topics include the topology for hyperspaces, examples of geometric models for hyperspaces, 2x and C(X) for Peano continua X, arcs in hyperspaces, the shape and contractability of hyperspaces, hyperspaces and the fixed point property, and Whitney maps. The text contains examples and exercises throughout, and provides proofs for most results.
Download or read book Direct Integral Theory written by O. A. Nielsen and published by CRC Press. This book was released on 2020-08-26 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers various topics related to direct integral theory, including Borel spaces, direct integral of Hilbert spaces and operators, direct integrals of representations, direct integrals and types of von Neumann algebras, and measures on the quasi-dual representations.
Download or read book Many Valued Topology and its Applications written by Ulrich Höhle and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 20th Century brought the rise of General Topology. It arose from the effort to establish a solid base for Analysis and it is intimately related to the success of set theory. Many Valued Topology and Its Applications seeks to extend the field by taking the monadic axioms of general topology seriously and continuing the theory of topological spaces as topological space objects within an almost completely ordered monad in a given base category C. The richness of this theory is shown by the fundamental fact that the category of topological space objects in a complete and cocomplete (epi, extremal mono)-category C is topological over C in the sense of J. Adamek, H. Herrlich, and G.E. Strecker. Moreover, a careful, categorical study of the most important topological notions and concepts is given - e.g., density, closedness of extremal subobjects, Hausdorff's separation axiom, regularity, and compactness. An interpretation of these structures, not only by the ordinary filter monad, but also by many valued filter monads, underlines the richness of the explained theory and gives rise to new concrete concepts of topological spaces - so-called many valued topological spaces. Hence, many valued topological spaces play a significant role in various fields of mathematics - e.g., in the theory of locales, convergence spaces, stochastic processes, and smooth Borel probability measures. In its first part, the book develops the necessary categorical basis for general topology. In the second part, the previously given categorical concepts are applied to monadic settings determined by many valued filter monads. The third part comprises various applications of many valued topologies to probability theory and statistics as well as to non-classical model theory. These applications illustrate the significance of many valued topology for further research work in these important fields.
