Abstract
In digital topology, it is well-known that, in 2D and in 3D, a digital set $X \subseteq Z^n$ is digitally well-composed (DWC), i.e., does not contain any critical configuration, if its immersion in the Khalimsky grids $H^n$ is well-composed in the sense of Alexandrov (AWC), i.e., its boundary is a disjoint union of discrete $(n-1)$-surfaces. We show that this is still true in $n$-D, $n \geq 2$, which is of prime importance since today 4D signals are more and more frequent.