Connectivity Preserving Multivalued Functions in Digital Topology

We study connectivity preserving 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 connectivity preserving multivalued functions, like continuous multivalued functions, are appropriate models for digital morpholological operations. Connectivity preservation, unlike continuity, is preserved by compositions, and generalizes easily to higher dimensions and arbitrary adjacency relations.