Abstract: In this paper, we prove that the two avours of well-compo- sedness called Continuous Well-Composedness (shortly CWCness), stat- ing that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (shortly DWCness), stating that a discrete set does not contain any critical con guration, are not equivalent in dimension 4. To prove this, we exhibit the example of a con- guration of 8 tesseracts (4D cubes) sharing a common corner (vertex), which is DWC but not CWC. This result is surprising since we know th...
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Topics: 
Combinatorics
Discrete mathematics
Pure mathematics