Search Results: the-theory-of-ultrafilters-grundlehren-der-mathematischen-wissenschaften

The theory of ultrafilters

Author: William Wistar Comfort,Stylianos Negrepontis

Publisher: Springer Verlag

ISBN: 9780387066042

Category: Mathematics

Page: 482

View: 876

The Theory of Ultrafilters

Author: William Wistar Comfort,S. Negrepontis

Publisher: Springer Science & Business Media

ISBN: 364265780X

Category: Mathematics

Page: 484

View: 4228

An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. From the first (logical) property arises its connection with two-valued logic and model theory; from the second (convergence) property arises its connection with topology and set theory. Both these descriptions of an ultrafilter are connected with compactness. The model-theoretic property finds its expression in the construction of the ultraproduct and the compactness type of theorem of Los (implying the compactness theorem of first-order logic); and the convergence property leads to the process of completion by the adjunction of an ideal element for every ultrafilter-i. e. , to the Stone-Cech com pactification process (implying the Tychonoff theorem on the compact ness of products). Since these are two ways of describing the same mathematical object, it is reasonable to expect that a study of ultrafilters from these points of view will yield results and methods which can be fruitfully crossbred. This unifying aspect is indeed what we have attempted to emphasize in the present work.

History of Topology

Author: I.M. James

Publisher: Elsevier

ISBN: 9780080534077

Category: Mathematics

Page: 1056

View: 2875

Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards. As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

The Theory of Ultrafilters

Author: William Wistar Comfort,Stylianos Negrepontis

Publisher: Springer Verlag

ISBN: N.A

Category: Ensembles, Théorie des

Page: 482

View: 9174

Handbook of Set-Theoretic Topology

Author: K. Kunen,J. Vaughan

Publisher: Elsevier

ISBN: 148329515X

Category: Mathematics

Page: 1282

View: 2450

This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Commutative Algebra

Noetherian and Non-Noetherian Perspectives

Author: Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson

Publisher: Springer Science & Business Media

ISBN: 9781441969903

Category: Mathematics

Page: 492

View: 2815

Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

The Stone-Čech Compactification

Author: R.C. Walker

Publisher: Springer Science & Business Media

ISBN: 3642619355

Category: Science

Page: 334

View: 1182

Recent research has produced a large number of results concerning the Stone-Cech compactification or involving it in a central manner. The goal of this volume is to make many of these results easily accessible by collecting them in a single source together with the necessary introductory material. The author's interest in this area had its origin in his fascination with the classic text Rings of Continuous Functions by Leonard Gillman and Meyer Jerison. This excellent synthesis of algebra and topology appeared in 1960 and did much to draw attention to the Stone-Cech compactification {3X as a tool to investigate the relationships between a space X and the rings C(X) and C*(X) of real-valued continuous functions. Although in the approach taken here {3X is viewed as the object of study rather than as a tool, the influence of Rings of Continuous Functions is clearly evident. Three introductory chapters make the book essentially self-contained and the exposition suitable for the student who has completed a first course in topology at the graduate level. The development of the Stone Cech compactification and the more specialized topological prerequisites are presented in the first chapter. The necessary material on Boolean algebras, including the Stone Representation Theorem, is developed in Chapter 2. A very basic introduction to category theory is presented in the beginning of Chapter 10 and the remainder of the chapter is an introduction to the methods of categorical topology as it relates to the Stone-Cech compactification.

Class Field Theory

Author: J. Neukirch

Publisher: Springer Science & Business Media

ISBN: 364282465X

Category: Mathematics

Page: 142

View: 5547

Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper spicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomol ogy, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group theoretical principle, admitting an entirely elementary description. This de scription makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep tion of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here.

Algebraic Number Theory

Author: Jürgen Neukirch

Publisher: Springer Science & Business Media

ISBN: 3662039834

Category: Mathematics

Page: 574

View: 9228

This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.

Acta Universitatis Carolinae

Mathematica et physica

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3605

Collected papers

Author: Erik K. van Douwen

Publisher: N.A

ISBN: 9780444816252

Category:

Page: 782

View: 3554

Open problems in topology

Author: J. van Mill,George M. Reed

Publisher: North Holland

ISBN: N.A

Category: Mathematics

Page: 692

View: 5571

From the Introduction: This volume grew from a discussion by the editors on the difficulty of finding good thesis problems for graduate students in topology. Although at any given time we each had our own favorite problems, we acknowledged the need to offer students a wider selection from which to choose a topic peculiar to their interests. One of us remarked, 'Wouldn't it be nice to have a book of current unsolved problems always available to pull down from the shelf?' The other replied 'Why don't we simply produce such a book?' Two years later and not so simply, here is the resulting volume. The intent is to provide not only a source book for thesis-level problems but also a challenge to the best researchers in the field.

Monographic Series

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category: Children's literature in series

Page: N.A

View: 8417

Questions and Answers in General Topology

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Topology

Page: N.A

View: 1493

Rozprawy Matematyczne

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1680

Extremal Phenomena in Certain Classes of Totally Bounded Groups

Author: William Wistar Comfort,Lewis C. Robertson

Publisher: N.A

ISBN: N.A

Category: Topological groups

Page: 48

View: 2990

Notices of the American Mathematical Society

Author: American Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7380

Proper and improper forcing

Author: Saharon Shelah

Publisher: Springer Verlag

ISBN: 9783540517009

Category: Mathematics

Page: 1020

View: 7314

The book deals with set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. Consequently, the theory of iterated forcing is developed. The author gives a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations. In addition to particular consistency results, the author shows methods which can be used for such independence results. Many of these are presented in an "axiomatic" framework (a la Martin's axiom) for this reason. The main aim of the book is thus to enable a researcher interested in an independence result of the approprate kind, to have much of the work done for him, thus allowing him to quote general results.

Categories and Sheaves

Author: Masaki Kashiwara,Pierre Schapira

Publisher: Springer Science & Business Media

ISBN: 3540279504

Category: Mathematics

Page: 498

View: 7237

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Handbook for Automatic Computation

Description of Algol 60

Author: Heinz Rutishauser,Friedrich L. Bauer

Publisher: Springer

ISBN: 3662381036

Category: Business & Economics

Page: 326

View: 5515

Find eBook