Continua, Decompositions, Manifolds PDF Download

Author: R. H. Bing
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 288

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Author:
Publisher: Academic Press
ISBN: 0080874436
Category : Mathematics
Languages : en
Pages : 331

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Decompositions of Manifolds

Author: Tom Eugene Knoblauch
Publisher:
ISBN:
Category :
Languages : en
Pages : 66

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Author: Steve Armentrout
Publisher: American Mathematical Soc.
ISBN: 0821818074
Category : Decomposition (Mathematics)
Languages : en
Pages : 76

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Author: Sergio Macias
Publisher: CRC Press
ISBN: 1420026534
Category : Mathematics
Languages : en
Pages : 374

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Book Description
Specialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology. In Topics on Continua, Sergio Macias, one of the field's leading scholars, presents four of his favorite continuum topics: inv

Author: Sibe Mardesic
Publisher: Springer
ISBN: 3540479759
Category : Mathematics
Languages : en
Pages : 266

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Book Description
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.

Author: Sergio Macías
Publisher: Springer
ISBN: 3319909029
Category : Mathematics
Languages : en
Pages : 451

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Book Description
This book is a significant companion text to the existing literature on continuum theory. It opens with background information of continuum theory, so often missing from the preceding publications, and then explores the following topics: inverse limits, the Jones set function T, homogenous continua, and n-fold hyperspaces. In this new edition of the book, the author builds on the aforementioned topics, including the unprecedented presentation of n-fold hyperspace suspensions and induced maps on n-fold hyperspaces. The first edition of the book has had a remarkable impact on the continuum theory community. After twelve years, this updated version will also prove to be an excellent resource within the field of topology.

Author: W.T. Ingram
Publisher: Springer Science & Business Media
ISBN: 146141797X
Category : Mathematics
Languages : en
Pages : 229

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Book Description
Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families. This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.

Author: Morton Brown
Publisher: American Mathematical Soc.
ISBN: 0821851233
Category : Mathematics
Languages : en
Pages : 194

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Book Description
This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Relationships between Continuum Theory and the Theory of Dynamical Systems, held at Humboldt State University in Arcata, California in June 1989. The conference reflected recent interactions between dynamical systems and continuum theory. Illustrating the increasing confluence of these two areas, this volume contains introductory papers accessible to mathematicians and graduate students in any area of mathematics, as well as papers aimed more at specialists. Most of the papers are concerned with the dynamics of surface homeomorphisms or of continua that occur as attractors for surface homeomorphisms.

Author: Sergio Macías
Publisher: Springer Nature
ISBN: 3030650812
Category : Mathematics
Languages : en
Pages : 225

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Book Description
This book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F. Burton Jones in the 1940s. It starts with a very solid introductory chapter, with all the prerequisite material for navigating through the rest of the book. It then gradually advances towards the main properties, Decomposition theorems, \mathcal{T}-closed sets, continuity and images, to modern applications. The set function \mathcal{T} has been used by many mathematicians as a tool to prove results about the semigroup structure of the continua, and about the existence of a metric continuum that cannot be mapped onto its cone or to characterize spheres. Nowadays, it has been used by topologists worldwide to investigate open problems in continuum theory. This book can be of interest to both advanced undergraduate and graduate students, and to experienced researchers as well. Its well-defined structure make this book suitable not only for self-study but also as support material to seminars on the subject. Its many open problems can potentially encourage mathematicians to contribute with further advancements in the field.