On the Segmentation of a Simple Closed Curve

Andrzej Trybulec

University of Bialystok

Summary.

The main goal of the work was to introduce the concept of the segmentation of a simple closed curve into (arbitrary small) arcs. The existence of it has been proved by Yatsuka Nakamura [21]. The concept of the gap of a segmentation is also introduced. It is the smallest distance between disjoint segments in the segmentation. For this purpose, the relationship between segments of an arc [24] and segments on a simple closed curve [21] has been shown.

This work has been partially supported by the CALCULEMUS grant HPRN-CT-2000-00102 and TYPES grant IST-1999-29001.

MML Identifier: JORDAN_A

Contents (PDF format)

1. Preliminaries
2. The Euclidean Distance
3. On the Distance between Subsets of a Euclidean Space
4. On the Segments
5. The Concept of a Segmentation
6. The Segments of a Segmentation
7. The Diameter of a Segmentation
8. The Concept of the Gap of a Segmentation

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