Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

## On the Decomposition of a Simple Closed Curve into Two Arcs

Andrzej Trybulec
University of Bialystok
This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102. The work has been done while the author visited Shinshu University.
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

The purpose of the paper is to prove lemmas needed for the Jordan curve theorem. The main result is that the decomposition of a simple closed curve into two arcs with the ends \$p_1, p_2\$ is unique in the sense that every arc on the curve with the same ends must be equal to one of them.

#### MML Identifier: JORDAN16

The terminology and notation used in this paper have been introduced in the following articles [25] [24] [27] [1] [26] [28] [3] [5] [9] [4] [22] [17] [21] [8] [7] [20] [2] [23] [15] [10] [6] [11] [19] [18] [12] [14] [13] [16]

Contents (PDF format)

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