Abstract: 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 $$(n-1)$$ ( 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.
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