Digital pseudomanifolds, digital weakmanifolds and Jordan–Brouwer separation theorem

An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps

“…In [15], the proof of the equivalence between the Euler formula and the hypermap Jordan property (consequently, the absence of Moebius band) is sketched (p. [23][24] using an induction on dart removing. This equivalence is presented in [15] (p. 21) and [17] (Theorem 2) as a Discrete Jordan Curve Theorem.…”

“…Indeed, the interest for discrete versions of the Jordan Curve Theorem has increased during the last years [23,29]. One reason is the irresistible development of digital computations on geometric objects in applicative domains, e.g.…”