Download or read book The Elements of Cantor Sets written by Robert W. Vallin and published by John Wiley & Sons. This book was released on 2013-07-29 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra. The author fills a gap in the current literature by providing an introductory and integrated perspective, thereby preparing readers for further study and building a deeper understanding of analysis, topology, set theory, number theory, and algebra. The Elements of Cantor Sets provides coverage of: Basic definitions and background theorems as well as comprehensive mathematical details A biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last century Chapter coverage of fractals and self-similar sets, sums of Cantor Sets, the role of Cantor Sets in creating pathological functions, p-adic numbers, and several generalizations of Cantor Sets A wide spectrum of topics from measure theory to the Monty Hall Problem An ideal text for courses in real analysis, topology, algebra, and set theory for undergraduate and graduate-level courses within mathematics, computer science, engineering, and physics departments, The Elements of Cantor Sets is also appropriate as a useful reference for researchers and secondary mathematics education majors.
Download or read book Intersections of Thick Cantor Sets written by Roger Kraft and published by American Mathematical Soc.. This book was released on 1992 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of thickness assigns to every Cantor set in the real line a number from 0 to [infinity symbol]. It was known that for some pairs of numbers the intersection of Cantor sets with such numbers as thicknesses may be just one point and that, in some other cases, with certain conditions, the intersection must contain a Cantor set. The author gives a complete answer to the problem of determining all pairs of thicknesses for which the intersection may be a single point and all the pairs of thicknesses for which the intersection must contain a Cantor set. He also considers the problem of how often, as one Cantor set is being translated over another one, the intersection of the two Cantor sets contains a Cantor set.
Download or read book The Philosophy of Set Theory written by Mary Tiles and published by Courier Corporation. This book was released on 2012-03-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div
Download or read book Cantor Minimal Systems written by Ian F. Putnam and published by American Mathematical Soc.. This book was released on 2018-05-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of Anatoly Vershik allowed for a combinatorial model, called the Bratteli-Vershik model, for such systems with no non-trivial closed invariant subsets. This model led to a construction of an ordered abelian group which is an algebraic invariant of the system providing a complete classification of such systems up to orbit equivalence. The goal of this book is to give a statement of this classification result and to develop ideas and techniques leading to it. Rather than being a comprehensive treatment of the area, this book is aimed at students and researchers trying to learn about some surprising connections between dynamics and algebra. The only background material needed is a basic course in group theory and a basic course in general topology.
Download or read book Fourier Analysis and Hausdorff Dimension written by Pertti Mattila and published by Cambridge University Press. This book was released on 2015-07-22 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern text examining the interplay between measure theory and Fourier analysis.
Download or read book Perspectives of Nonlinear Dynamics Volume 1 written by E. Atlee Jackson and published by CUP Archive. This book was released on 1989 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
Download or read book Cantorian Set Theory and Limitation of Size written by Michael Hallett and published by Oxford University Press. This book was released on 1986 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Download or read book Embedding Cantor Sets in Manifolds written by Richard Paul Osborne and published by . This book was released on 1965 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proofs of the Cantor Bernstein Theorem written by Arie Hinkis and published by Springer Science & Business Media. This book was released on 2013-02-26 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for the historiography of mathematics.
Download or read book Cantor Sets and Homotopy Connectedness of Manifolds written by David Grant Wright and published by . This book was released on 1973 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Topology in Dimensions 2 and 3 written by E.E. Moise and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 1997 with total page 1452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topological and Measure theoretic Studies on Cantor Sets and Peano Spaces written by Alan H. Schoenfeld and published by . This book was released on 1973 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Problems in Analysis written by Robert C. Gunning and published by Princeton University Press. This book was released on 2015-03-08 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume reflects both the diversity of Bochner's pursuits in pure mathematics and the influence his example and thought have had upon contemporary researchers. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Ergodic Theory and Dynamical Systems written by Idris Assani and published by Walter de Gruyter. This book was released on 2013-12-12 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill. The articles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, and algebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.
Download or read book Real Mathematical Analysis written by Charles C. Pugh and published by Springer Science & Business Media. This book was released on 2003-11-14 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Download or read book The Foundations of Topological Analysis A Straightforward Introduction written by K. G. Binmore and published by Cambridge University Press. This book was released on 1981-05-07 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the ideas from general topology that are used in elementary analysis. It is written at a level that is intended to make the bulk of the material accessible to students in the latter part of their first year of study at a university or college although students will normally meet most of the work in their second or later years. The aim has been to bridge the gap between introductory books like the author's Mathematical Analysis: A Straightforward Approach, in which carefully selected theorems are discussed at length with numerous examples, and the more advanced book on analysis, in which the author is more concerned with providing a comprehensive and elegant theory than in smoothing the ways for beginners. An attempt has been made throughout not only to prepare the ground for more advanced work, but also to revise and to illuminate the material which students will have met previously but may have not fully understood.
