Abstract : We discuss an Alexandroff topology on ℤ2 having the property that its quotient topologies include the Khalimsky and Marcus-Wyse topologies. We introduce a further quotient topology and prove a Jordan curve theorem for it.
Josef Šlapal. Topological structuring of the digital plane. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 2 (2), pp.165--176. ⟨10.46298/dmtcs.601⟩. ⟨hal-00980765⟩