Digital topology is an important tool in computer graphics and image processing. Until the work of Khalimsky et al. in the early 1990s, it was mainly an ad hoc affair, using graph-theoretic techniques; Khalimsky and his coauthors, in their many papers, introduced techniques from abstract topology restricted to the set of points in the real plane having integer coordinates.

This paper takes the abstract approach a step further, by using a weakened version of Kuratowski closure operations to define a generalization of classical topologies more suitable to this setting, and sophisticated enough to prove an analog of the Jordan curve theorem (JCT) (the classical JCT says that every simple closed curve divides the real plane into precisely two components: an “inside” and an “outside”).

The paper is highly mathematical, and does not go into specific applications in computer science.