RESULTS ON FINITE COLLECTION OF POLYGONS AND A PROOF OF THE JORDAN CURVE THEOREM

Article Type

Research Article

Publication Title

Mathematics Student

Abstract

We introduce the notion of polygons and Jordan curves. We first provide a proof of the Jordan Curve Theorem for polygons, and then we answer the following questions: given a finite collection of polygonal regions in the plane, can we write their union as an almost disjoint union of polygonal regions? What do the boundaries of the connected components in the complement of these polygons look like? Having answered these questions, we construct a "regular" polygonal cover for arcs in the plane and use such a covering to prove a separation result about arcs inside discs. In the last section we provide a proof of the Jordan Curve Theorem using the methods developed in the previous sections.

First Page

87

Last Page

125

Publication Date

7-1-2022

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