Alternate version of continuity for digital multivalued functions

We introduce weakly continuous multivalued functions between digital images. This notion generalizes that of continuous multivalued functions studied mostly in the setting of the digital plane $Z^2$. We show that weakly continuous multivalued functions, like continuous multivalued functions, are appropriate models for digital morpholological operations. Weak continuity, unlike continuity, is preserved by compositions, and generalizes easily to higher dimensions and arbitrary adjacency relations.