An Elementary Proof of the Jordan-schoenflies Theorem1

Abstract

The exterior of a bounded closed point set b in E will mean the unbounded region of the complementary set E — b. The remainder of E — b, if not vacuous, will be called the interior of b. (A) As a corollary to the above theorem, c is intersected by any simple arc with one end point interior and one exterior to c. This paper contains an elementary constructive proof of the Jordan-Schoenflies Theorem, motivated by the belief that such a proof should be presented at a fairly early stage to students of topology and analysis. To that end, it is desirable that the argument be disassociated from conformai mapping theory and be accomplished by methods as elementary as possible.

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