On the Simple Closed Curve Property of the Circle and the Fashoda Meet Theorem for It

Yatsuka Nakamura

Shinshu University, Nagano

Summary.

First, we prove the fact that the circle is the simple closed curve, which was defined as a curve homeomorphic to the square. For this proof, we introduce a mapping which is a homeomorphism from 2-dimensional plane to itself. This mapping maps the square to the circle. Secondly, we prove the Fashoda meet theorem for the circle using this homeomorphism.

MML Identifier: JGRAPH_3

Contents (PDF format)

1. Preliminaries
2. The Circle is a Simple Closed Curve
3. The Fashoda Meet Theorem for the Circle

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