On the locally uniform openness of polyhedral sets (Q5954623)

The author proves that unions of finitely many polyhedrons have a property which he calls local uniform openness. A consequence of this property is that any set-valued map defined on such a polyhedral set is locally Lipschitz if it is locally Lipschitz on each component of the set. The author's nice approach is geometrically perspicuous where there also seems to be a relationship between the local uniform openness property and Lipschitzian manifolds.