Download or read book Characterizing k Dimensional Universal Menger Compacta written by Mladen Bestvina and published by American Mathematical Soc.. This book was released on 1988 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir considers only the case of compact Menger-space-manifolds. With routine changes (open covers instead of epsilonics), the results are valid for non-compact Menger-space-manifolds. Also outlined are parts of proofs for the non-compact case that are substantially different from the compact case.
Download or read book Encyclopedia of General Topology written by K.P. Hart and published by Elsevier. This book was released on 2003-11-18 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms
Download or read book Continua written by Howard Cook and published by CRC Press. This book was released on 2020-12-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the special session on Modern Methods in Continuum Theory presented at the 100th Annual Joint Mathematics Meetings held in Cincinnati, Ohio. It also features the Houston Problem Book which includes a recently updated set of 200 problems accumulated over several years at the University of Houston.;These proceedings and problems are aimed at pure and applied mathematicians, topologists, geometers, physicists and graduate-level students in these disciplines.
Download or read book Characterization and Topological Rigidity of Nobeling Manifolds written by Andrzej Nagórko and published by American Mathematical Soc.. This book was released on 2013-04-22 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a theory of Nobeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nobeling manifold characterization conjecture.
Download or read book Geometric Aspects of General Topology written by Katsuro Sakai and published by Springer Science & Business Media. This book was released on 2013-07-22 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.
Download or read book Erdos Space and Homeomorphism Groups of Manifolds written by Jan Jakobus Dijkstra and published by American Mathematical Soc.. This book was released on 2010 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group H(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. We present a complete solution to the topological classification problem for H(M,D) as follows. If M is a one-dimensional topological manifold, then we proved in an earlier paper that H(M,D) is homeomorphic to Qω, the countable power of the space of rational numbers. In all other cases we find in this paper that H(M,D) is homeomorphic to the famed Erdős space E E, which consists of the vectors in Hilbert space l2 with rational coordinates. We obtain the second result by developing topological characterizations of Erdős space.
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 642 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 theory are primarily used for the study of these spaces. The mix of methods from several disciplines makes the subject particularly 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 in infinite-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 the Dobrowolski-Marciszewski-Mogilski Theorem, linking the results 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 for graduate 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 therefore more suitable as a text for a research seminar. The book consequently has the character of both textbook and a research monograph. In Chapters 1 through 5, unless stated otherwise, all spaces under discussion are separable and metrizable. 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 there 3) 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 Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Download or read book Recent Progress in General Topology written by M. Husek and published by Elsevier. This book was released on 1992-11-20 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.
Download or read book Topology and Its Applications written by Sergeĭ Petrovich Novikov and published by American Mathematical Soc.. This book was released on 1993 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of an international topology conference - this book covrs various aspects of general algebraic, and low-dimensional topology.
Download or read book Glasnik Matematicki written by and published by . This book was released on 1996-12 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Open Problems in Topology II written by Elliott M. Pearl and published by Elsevier. This book was released on 2011-08-11 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world
Download or read book Recent Progress in General Topology III written by K.P. Hart and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 903 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Download or read book Handbook of the History of General Topology written by C.E. Aull and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1989-06 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Topology and Shape Theory written by Sibe Mardesic and published by Springer. This book was released on 2006-11-14 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
