Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

## 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

The terminology and notation used in this paper have been introduced in the following articles [16] [19] [1] [17] [12] [9] [20] [8] [3] [5] [10] [2] [7] [13] [15] [18] [4] [6] [14] [11]

#### 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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