A Decomposition of Simple Closed Curves and the Order of Their Points

Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

A Decomposition of Simple Closed Curves and the Order of Their Points

Yatsuka Nakamura: Shinshu University, Nagano
Andrzej Trybulec: University of Bialystok

Summary.

The goal of the article is to introduce an order on a simple closed curve. To do this, we fix two points on the curve and devide it into two arcs. We prove that such a decomposition is unique. Other auxiliary theorems about arcs are proven for preparation of the proof of the above.

MML Identifier: JORDAN6

The terminology and notation used in this paper have been introduced in the following articles [18] [21] [1] [20] [12] [17] [22] [3] [4] [9] [10] [15] [8] [16] [6] [19] [7] [13] [2] [14] [11] [5]

Contents (PDF format)

Middle Points of Arcs
Segments of Arcs
Decomposition of a Simple Closed Curve Into Two Arcs
Uniqueness of Decomposition of a Simple Closed Curve
Lower Arcs and Upper Arcs
An Order of Points in a Simple Closed Curve

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Received December 19, 1997

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