Abstract : In digital topology, it is well-known that, in 2D and in 3D, a set is digitally well-composed (DWC), that is, does not contain any critical configuration, iff its immersion in the Khalimsky grids is well-composed in the Alexandrov sense (AWC), that is, its topological boundary is a disjoint union of discrete surfaces. This report shows that this is still true in any finite dimension, which is of primary importance since today 4D signals are more and more frequent. This means that the usual digital subsets of Z^n that are DWC can be immersed in the Khalimsky grids and the connected components of their boundaries will be discrete surfaces. Conversely, if any subset verifies that its immersion is AWC, we will know that this set is DWC. Note that the correctness of this proof is still not verified.