Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

## On the Dividing Function of the Simple Closed Curve into Segments

Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

At the beginning, the concept of the segment of the simple closed curve in 2-dimensional Euclidean space is defined. Some properties of segments are shown in the succeeding theorems. At the end, the existence of the function which can divide the simple closed curve into segments is shown. We can make the diameter of segments as small as we want.

#### MML Identifier: JORDAN7

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

#### Contents (PDF format)

1. Definition of the Segment and Its Property
2. A Function to Divide the Simple Closed Curve

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