Topological dimension and dynamical systems [electronic resource] / Michel Coornaert.
Coornaert, M. (Michel), author.
2015
QA611.5
Available Online

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Title Topological dimension and dynamical systems [electronic resource] / Michel Coornaert.
Author Coornaert, M. (Michel), author.
Uniform Title Dimension topologique et systèmes dynamiques. English
ISBN 9783319197944 electronic book
3319197940 electronic book
9783319197937
DOI https://doi.org/10.1007/978-3-319-19794-4
Published Cham : Springer, 2015.
Language English
Description 1 online resource (xv, 233 pages) : illustrations.
Item Number 10.1007/978-3-319-19794-4 doi
Call Number QA611.5
Dewey Decimal Classification 515/.39
Summary Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner's characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.
Note "This is a revised and augmented English edition of my book "Dimension topologique et systèmes dynamiques" which was published in 2005 by the Société Mathématique de France."
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 26, 2015).
Series Universitext.
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Record Appears in Online Resources > Ebooks
All Resources
Topological Dimension
Zero-Dimensional Spaces
Topological Dimension of Polyhedra
Dimension and Maps
Some Classical Counterexamples
Mean Topological Dimension for Continuous Maps
Shifts and Subshifts over Z
Applications of Mean Dimension to Embedding Problems
Amenable Groups
Mean Topological Dimension for Actions of Amenable Groups.

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