Topologies on the group of homeomorphisms of a Cantor set

Sergey Bezuglyi; Anthony H. Dooley; Jan Kwiatkowski

Topologies on the group of homeomorphisms of a Cantor set

Sergey Bezuglyi
, Anthony H. Dooley
, Jan Kwiatkowski

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let $\Homeo(\Omega)$ be the group of all homeomorphisms of a Cantor set $\Omega$. We study topological properties of $\Homeo(\Omega)$ and its subsets with respect to the uniform $(\tau)$ and weak $(\tau_w)$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in $\tau$ and $\tau_w$ are found.

Original language	English
Pages (from-to)	299-332
Journal	Topological Methods in Nonlinear Analysis
Volume	27
Issue number	2
Publication status	Published - Jun 2006

Cite this

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title = "Topologies on the group of homeomorphisms of a Cantor set",

abstract = "Let \$\textbackslash{}Homeo(\textbackslash{}Omega)\$ be the group of all homeomorphisms of a Cantor set \$\textbackslash{}Omega\$. We study topological properties of \$\textbackslash{}Homeo(\textbackslash{}Omega)\$ and its subsets with respect to the uniform \$(\textbackslash{}tau)\$ and weak \$(\textbackslash{}tau\_w)\$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in \$\textbackslash{}tau\$ and \$\textbackslash{}tau\_w\$ are found. ",

author = "Sergey Bezuglyi and Dooley, \{Anthony H.\} and Jan Kwiatkowski",

year = "2006",

month = jun,

language = "English",

volume = "27",

pages = "299--332",

journal = "Topological Methods in Nonlinear Analysis",

issn = "1230-3429",

publisher = "Juliusz Schauder Center for Nonlinear Analysis",

number = "2",

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TY - JOUR

T1 - Topologies on the group of homeomorphisms of a Cantor set

AU - Bezuglyi, Sergey

AU - Dooley, Anthony H.

AU - Kwiatkowski, Jan

PY - 2006/6

Y1 - 2006/6

N2 - Let $\Homeo(\Omega)$ be the group of all homeomorphisms of a Cantor set $\Omega$. We study topological properties of $\Homeo(\Omega)$ and its subsets with respect to the uniform $(\tau)$ and weak $(\tau_w)$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in $\tau$ and $\tau_w$ are found.

AB - Let $\Homeo(\Omega)$ be the group of all homeomorphisms of a Cantor set $\Omega$. We study topological properties of $\Homeo(\Omega)$ and its subsets with respect to the uniform $(\tau)$ and weak $(\tau_w)$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in $\tau$ and $\tau_w$ are found.

UR - http://arxiv.org/abs/math/0410507

M3 - Article

SN - 1230-3429

VL - 27

SP - 299

EP - 332

JO - Topological Methods in Nonlinear Analysis

JF - Topological Methods in Nonlinear Analysis

IS - 2

ER -

Topologies on the group of homeomorphisms of a Cantor set

Abstract

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