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Almost totally disconnected minimal systems

Published online by Cambridge University Press:  01 June 2009

FRANCISCO BALIBREA ,
TOMASZ DOWNAROWICZ ,
ROMAN HRIC ,
L’UBOMÍR SNOHA  and
VLADIMÍR ŠPITALSKÝ
FRANCISCO BALIBREA
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, Aptdo. de Correos 4021, E–30100 Murcia, Spain (email: balibrea@um.es)
TOMASZ DOWNAROWICZ
Affiliation:
Institute of Mathematics, Technical University, Wybrzeze Wyspiańskiego 27, 50-370 Wroclaw, Poland (email: downar@im.pwr.wroc.pl)
ROMAN HRIC
Affiliation:
Laboratoire Analyse, Géométrie et Applications, Institut Galilée, Université Paris 13, 99, Avenue Jean-Baptiste Clément, 93430 Villetaneuse, France Institute of Mathematics and Computer Science, Science and Research Institute, Matej Bel University, Dumbierska 1, SK-974 11 Banská Bystrica, Slovakia (email: hric@math.univ-paris13.fr, hric@savbb.sk)
L’UBOMÍR SNOHA
Affiliation:
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK–974 01 Banská Bystrica, Slovakia (email: snoha@fpv.umb.sk, spitalsk@fpv.umb.sk)
VLADIMÍR ŠPITALSKÝ
Affiliation:
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK–974 01 Banská Bystrica, Slovakia (email: snoha@fpv.umb.sk, spitalsk@fpv.umb.sk)
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Abstract

A space X is said to be almost totally disconnected if the set of its degenerate components is dense in X. We prove that an almost totally disconnected compact metric space admits a minimal map if and only if either it is a finite set or it has no isolated point. As a consequence we obtain a characterization of minimal sets on dendrites and local dendrites.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 3 , June 2009 , pp. 737 - 766
Copyright
Copyright © Cambridge University Press 2009

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