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

On the General Position of Special Polygons

Mariusz Giero
University of Bialystok

Summary.

In this paper we introduce the notion of general position. We also show some auxiliary theorems for proving Jordan curve theorem. The following main theorems are proved: \begin{enumerate} \item End points of a polygon are in the same component of a complement of another polygon if number of common points of these polygons is even; \item Two points of polygon $L$ are in the same component of a complement of polygon $M$ if two points of polygon $M$ are in the same component of polygon $L.$ \end{enumerate}

This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102.

MML Identifier: JORDAN12

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

Contents (PDF format)

1. Preliminaries
2. The Notion of General Position and Its Properties
3. Properties of Being in the Same Component of a Complement of a Polygon
4. Cells Are Convex
5. Properties of Points Lying on the Same Line
6. The Position of the Points of a Polygon with Respect to Another Polygon

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