Digital geometry may not be discrete

Abstract As is often done in set theory we identify sets with their characteristics functions. A consistent use of functional notations in digital geometry has a few distinct advantages over the conventional approach: digital geometry is truly imbedded into the customary topology, e.g., digital images, being sets in themselves, all have continuous analogs; images are digitally connected if they are connected; the same notion of connectedness applies to an image and its complementary image; color images are naturally included into the same general framework; and, digitization is a projection from the set of analog images onto the subset of digital images.