A 4D counter-example showing that DWCness does not imply CWCness in \(n\)D (Q2037375)

The authors prove that the two flavours of well-composedness called Continuous Well-Composed (CWCness for brevity), satisfying that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (DWCness), stating that a discrete set does not contain any critical configuration, are not equivalent in dimension 4. Indeed, this finding is quite meaningful because in 2D and 3D CWCness is equivalent to DWCness. To prove this observation, the authors use some tools such as homology, homotopy, homotopy equivalence, and finally they suggest some examples to prove the non-equivalence between CWCness and DWCness in 4D. For the entire collection see [Zbl 1464.68015].