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Acta Mathematica Vietnamica

ON THE LOCALLY UNIFORM OPENNESS OF POLYHEDRAL SETS

icon-email HUYNH THE PHUNG

Abstract

The paper is concerned with a geometrical property of polyhedral sets. Specifically, we shall prove that every polyhedral set (denoted by M) is locally uniformly opening. As a consequence, we show that for any set-valued map F defined on a polyhedral set M, F is locally Lipschitz on M iff it is locally Lipschitz on each component of M.