Continuous Well-Composedness Implies Digital Well-Composedness in n -D

In this paper, we prove that when a n -D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological (n-1) -manifold, then it is digitally well-composed (DWC), which means that it does not contain any critical configuration. We prove this result thanks to local homology. This paper is the sequel of a previous paper where we proved that DWCness does not imply CWCness in 4D.