Characterization of the deletion of (26,6)(26,6)-simple points as multivalued (N,26)(N,26)-retractions

In previous papers we have introduced a notion of multivalued continuity in digital spaces which extends the usual notion of digital continuity and allows us to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points in 2-D, one of the most important processing operations in digital topology, as a particular kind of retraction. In this work we extend this result to three-dimensional digital sets, characterizing the deletion of (26,6)(26,6)-simple points in 3-D as (N,26)(N,26)-retractions.