On the Rectangular Finite Sequences of the Points of the Plane

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)

General preliminaries
Preliminaries (general topology)
Preliminaries (the topology of the plane)
Special points of a compact non empty subset of the plane
Subsets of the plane that are neither vertical nor horizontal
A special sequence related to a compact non empty subset of the plane
Rectangular finite suequences of the points of the plane
Jordan property

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Received November 30, 1997

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