  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.
