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

## On the Components of the Complement of a Special Polygonal Curve

Andrzej Trybulec
University of Bialystok
The work had been done when the first author visited Nagano in fall of 1998.
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

By the special polygonal curve we meana simple closed curve, that is a polygone and moreover has edges parallel to axes. We continue the formalization of the Takeuti-Nakamura proof [12] of the Jordan curve theorem. In the paper we prove that the complement of the special polygonal curve consists of at least two components. With the theorem which has at most two components we completed the theorem that a special polygonal curve cuts the plane into exactly two components.

#### MML Identifier: SPRECT_4

The terminology and notation used in this paper have been introduced in the following articles [13] [1] [3] [2] [16] [8] [11] [5] [6] [4] [15] [10] [14] [9] [7]

Contents (PDF format)

#### Bibliography

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