Local homeomorphisms that *-commute with the shift

Paulette N. Willis

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arXiv · 1010.5739

Local homeomorphisms that *-commute with the shift

Paulette N. Willis

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Abstract

Exel and Renault proved that a sliding block code on a one-sided shift space coming from a progressive block map is a local homeomorphism. We provide a counterexample showing that the converse does not hold. We use this example to generalize the notion of progressive to a property of block maps we call weakly progressive, and we prove that a sliding block code coming from a weakly progressive block map is a local homeomorphism. We also introduce the notion of a regressive block map and prove that a sliding block code *-commutes with the shift map if and only if it comes from a regressive block map. We also prove that a sliding block code is a local homeomorphism and *-commutes with the shift map if and only if it is a k-fold covering map defined from a regressive block map.

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Paulette N. Willis. 2010-10-27. Local homeomorphisms that *-commute with the shift. https://arxiv.org/abs/1010.5739

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