Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

## On the Rectangular Finite Sequences of the Points of the Plane

Andrzej Trybulec
University of Bialystok
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

The article deals with a rather technical concept - rectangular sequences of the points of the plane. We mean by that a finite sequence consisting of five elements, that is circular, i.e. the first element and the fifth one of it are equal, and such that the polygon determined by it is a non degenerated rectangle, with sides parallel to axes. The main result is that for the rectangle determined by such a sequence the left and the right component of the complement of it are different and disjoint.

#### MML Identifier: SPRECT_1

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

#### Contents (PDF format)

1. General preliminaries
2. Preliminaries (general topology)
3. Preliminaries (the topology of the plane)
4. Special points of a compact non empty subset of the plane
5. Subsets of the plane that are neither vertical nor horizontal
6. A special sequence related to a compact non empty subset of the plane
7. Rectangular finite suequences of the points of the plane
8. Jordan property

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