Dimension Theory
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Modern Dimension Theory
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Author : Jun-Iti Nagata
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Modern Dimension Theory written by Jun-Iti Nagata and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Bibliotheca Mathematica, Volume 6: Modern Dimension Theory provides a brief account of dimension theory as it has been developed since 1941, including the principal results of the classical theory for separable metric spaces. This book discusses the decomposition theorem, Baire's zero-dimensional spaces, dimension of separable metric spaces, and characterization of dimension by a sequence of coverings. The imbedding of countable-dimensional spaces, sum theorem for strong inductive dimension, and cohomology group of a topological space are also elaborated. This text likewise covers the uniformly zero-dimensional mappings, theorems in euclidean space, transfinite inductive dimension, and dimension of non-metrizable spaces. This volume is recommended to students and specialists researching on dimension theory.
Dimension Theory
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Author : Michael G. Charalambous
language : en
Publisher: Springer Nature
Release Date : 2019-10-08
Dimension Theory written by Michael G. Charalambous and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.
This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Dimension Theory In Dynamical Systems
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Author : Yakov B. Pesin
language : en
Publisher: University of Chicago Press
Release Date : 2008-04-15
Dimension Theory In Dynamical Systems written by Yakov B. Pesin and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-15 with Mathematics categories.
The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.
Dimension Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 1970-05-31
Dimension Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970-05-31 with Mathematics categories.
Dimension Theory
Dimension Theory For Nonsingular Injective Modules
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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
Dimension Theory For Nonsingular Injective Modules written by K. R. Goodearl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
This paper has two major purposes: to develop a theory of types for the category of nonsingular injective modules over an arbitrary ring, and to construct dimension functions which determine the isomorphism classes of the nonsingular injective modules.
Dimension Theory Pms 4 Volume 4
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Author : Witold Hurewicz
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Dimension Theory Pms 4 Volume 4 written by Witold Hurewicz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
Book 4 in the Princeton Mathematical Series. Originally published in 1941. 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.
Fractals And Universal Spaces In Dimension Theory
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Author : Stephen Lipscomb
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Fractals And Universal Spaces In Dimension Theory written by Stephen Lipscomb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-28 with Mathematics categories.
Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.
The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality written by K. R. Goodearl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
Dimension Theory
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Author : Witold Hurewicz
language : en
Publisher:
Release Date : 1969
Dimension Theory written by Witold Hurewicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Dimension theory (Topology). categories.
Dimension Theory Of General Spaces
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Author : A. R. Pears
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-08
Dimension Theory Of General Spaces written by A. R. Pears and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-08 with Mathematics categories.
A complete and self-contained account of the dimension theory of general topological spaces, with particular emphasis on the dimensional properties of non-metrizable spaces. It makes the subject accessible to beginning graduate students and will also serve as a reference work for general topologists. Two introductory chapters summarize standard results in general topology, and cover material on paracompactness and metrization. The principal definitions of dimension follow and their general properties are deduced. Many examples are analysed to show some of the more surprising or pathological aspects of dimension theory. Wherever it is useful to do so, proofs are given in detail.