Jordan Curve Theorem, Proof

JCT - Sources

Scott E. Brodie, MD, PhD
Icahn School of Medicine at Mount Sinai
New York

Our proof of Jordan Separation for Polygons follows Courant and Robbins, "What is Mathematics? An Elementary Approach to Ideas and Methods."
The connection between $K_{3,3}\;$ and JCT is derived from Thomassen (1992), "The Jordan-Schonflies Theorem and the Classification of Surfaces"
The treatment of the Crossed Arcs Lemma simplifies the proof of Maehara (1984), "The Jordan Curve theorem via the Brouwer Fixed Point Theorem." (Maehara deduces the Crossed Ars Lemma and JAT from the Brouwer Fixed Point Theorem and the Tietze Extension Theorem.)
The treatment of the Jordan Arc Theorem is derived from Moise, "Geometric topology in dimensions 2 and 3," (hopefully) modified for clarity.

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