Almost totally disconnected minimal systems
- 1 June 2009
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 29 (3) , 737-766
Abstract
A spaceXis said to be almost totally disconnected if the set of its degenerate components is dense inX. 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.Keywords
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