A Jordan Curve Theorem with Respect to Certain Closure Operations on the Digital Plane
Josef Šlapal · Electronic Notes in Theoretical Computer Science · 2001
The closure operations on Z × Z introduced and studied in the paper generalize the Khalimsky topology, which is commonly used as a basic topological structure in digital topology nowadays. By proving a digital analogy of the Jordan curve theorem for these closure operations, we show that they are also suitable for solving problems of digital topology. We mention some advantages of the closure operations studied over the Khalimsky topology.