Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

**Mariusz Giero**- University of Bialystok

- 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.

- Preliminaries
- The Notion of General Position and Its Properties
- Properties of Being in the Same Component of a Complement of a Polygon
- Cells Are Convex
- Properties of Points Lying on the Same Line
- The Position of the Points of a Polygon with Respect to Another Polygon

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