Digital Jordan Curve Theorems
نویسنده
چکیده
Efim Khalimsky’s digital Jordan curve theorem states that the complement of a Jordan curve in the digital plane equipped with the Khalimsky topology has exactly two connectivity components. We present a new, short proof of this theorem using induction on the Euclidean length of the curve. We also prove that the theorem holds with another topology on the digital plane but then only for a restricted class
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