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Adopting the point-neighbourhood definition of topology, which we think may in some cases help acquire a very good insight of digital topologies, we unify the proof technique of the results on 4-connectedness and on 8-connectedness in 2. We also show that there is no topology compatible with 6-connectedness. We shortly comment on potential further use of this approach.

Digital topologies revisited: An approach based on the topological point-neighbourhood