
doi: 10.32092/1154
After some background, at first we prove the equivalence between two definitions of “Jordan’s curve”, defined as simple and closed plane curve but known also as subset of R2 homeomorphic to a circle. Using the ideas of Maehara ([6]) who gave a proof of Jordan’s classical theorem, for a given Jordan’s curve Γ we introduce the notions of central point, internal set, external set, all inspired by the special case in which Γ is a circle; we show that such sets are open and “arc-connected”, the first one being bounded and the second one unbounded; moreover, we show that the curve Γ is the boundary of both of them, and, finally, that they constitute a partition of R2 \ Γ. Obviously, these results include a revisitation of the proof of Jordan’s theorem. In the final section we give an explicit construction of an example of homeomorphism between a circle and the boundary of a triangle.
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