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Universitext

Topological Dimension and Dynamical Systems

Authors: Coornaert, Michel

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  • Provides an accessible introduction to difficult material previously only found scattered in literature
  • Provides a detailed exposition of the elements of dimension theory for topological spaces and dynamical systems
  • Contains 160 exercises, of which helpful hints are provided for the most challenging
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eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-19794-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-19793-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Professor Michel Coornaert teaches at the University of Strasbourg. He is the author of many Springer volumes including Cellular Automata and Groups (2010), Symbolic Dynamics and Hyperbolic Groups (1993) and Geometrie et theorie des groupes (1990).

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-19794-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-19793-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topological Dimension and Dynamical Systems
Authors
Series Title
Universitext
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-19794-4
DOI
10.1007/978-3-319-19794-4
Softcover ISBN
978-3-319-19793-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XV, 233
Number of Illustrations
12 b/w illustrations, 1 illustrations in colour
Additional Information
Original French edition published by Société Mathématique de France, Paris, 2005
Topics