Digital Jordan curves. (English) Zbl 1111.54021
An Alexandroff topology is defined on the set \(\mathbb Z^{2}\) of integer lattice points of the Euclidean plane \(\mathbb R^{2}\). This topology has the advantage over the usual Khalimsky topology on \(\mathbb Z^{2}\) in that any cycle of a certain square-diagonal graph of type 4 is a digital Jordan curve in the comparability graph induced by the specialization order (defined by \(x\leq y\) if and only if \(x\in\text{ cl}(y)\)) of the topology. However, the topology is not the product of two topologies on \(\mathbb Z\).
Reviewer: Richard G. Wilson (México)
MSC:
54D05 | Connected and locally connected spaces (general aspects) |
54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
05C38 | Paths and cycles |
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