Digital Topology and Geometry:

an Axiomatic Approach with Applications to GIS and Spatial Reasoning.

Some recent papers

M.B. Smyth and R. Tsaur. Hyperconvex semi-metric spaces. Topology Proc., 26:791--810, 2001--2002. (PostScript | PDF)

M.B. Smyth and R. Tsaur. AFPP vs FPP: the link between almost fixed point properties of discrete structures and fixed point properties of spaces. Appl. Categ. Structures, 11:95--116, 2003. (PostScript | PDF)

R. Tsaur and M.B. Smyth. Fixed points in digital topology (via Helly posets). Electron. Notes Theor. Comput. Sci., 74, 2003. (PostScript | PDF)

(A fuller list of some recent papers, but without descriptions, is here.)