LEADER 04074nam 22006615 450 001 9910299772003321 005 20200705191717.0 010 $a3-319-19794-0 024 7 $a10.1007/978-3-319-19794-4 035 $a(CKB)3710000000436884 035 $a(SSID)ssj0001558644 035 $a(PQKBManifestationID)16183078 035 $a(PQKBTitleCode)TC0001558644 035 $a(PQKBWorkID)14818765 035 $a(PQKB)11132089 035 $a(DE-He213)978-3-319-19794-4 035 $a(MiAaPQ)EBC6315738 035 $a(MiAaPQ)EBC5579377 035 $a(Au-PeEL)EBL5579377 035 $a(OCoLC)911920025 035 $a(PPN)186400292 035 $a(EXLCZ)993710000000436884 100 $a20150620d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTopological Dimension and Dynamical Systems /$fby Michel Coornaert 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XV, 233 p. 13 illus., 1 illus. in color.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-19793-2 320 $aIncludes bibliographical references and index. 327 $aTopological 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. 330 $aTranslated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner?s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored. 410 0$aUniversitext,$x0172-5939 606 $aDynamics 606 $aErgodic theory 606 $aTopology 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aTopology. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aTopology. 676 $a515.39 700 $aCoornaert$b Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut$059545 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299772003321 996 $aTopological dimension and dynamical systems$91522693 997 $aUNINA