Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

## Cages - the External Approximation of Jordan's Curve

Czeslaw Bylinski
University of Bialystok
The paper was started during the author's visit in the Shinshu University, Nagano, Japan, summer 1998.
Mariusz Zynel
University of Bialystok
The paper was finished during the author's visit in the Shinshu University, Nagano, Japan, summer 1999.

### Summary.

On the Euclidean plane Jordan's curve may be approximated with a polygonal path of sides parallel to coordinate axes, either externally, or internally. The paper deals with the external approximation, and the existence of a {\em Cage} - an external polygonal path - is proved.

#### MML Identifier: JORDAN9

The terminology and notation used in this paper have been introduced in the following articles [25] [30] [21] [3] [27] [2] [22] [31] [6] [7] [1] [4] [8] [29] [9] [18] [16] [17] [24] [32] [13] [23] [5] [14] [15] [19] [20] [12] [28] [26] [10] [11]

#### Contents (PDF format)

1. Generalities
2. Go-Board Preliminaries
3. Cages

#### Acknowledgments

Thanks are due to Professor Yatsuka Nakamura and people in the Kiso Laboratory for their gracious support during the work on this paper. Authors would like also to express their gratitude to Andrzej Trybulec for his help in preparing the paper.

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Received June 22, 1999
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