Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

## The Topological Space $\calE^2_\rmT$. Arcs, Line Segments and Special Polygonal Arcs

Agata Darmochwal
Warsaw University, Bialystok
The article was written during my work at Shinshu University, 1991.
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

The notions of arc and line segment are introduced in two-dimensional topological real space ${\cal E}^2_{\rm T}$. Some basic theorems for these notions are proved. Using line segments, the notion of special polygonal arc is defined. It has been shown that any special polygonal arc is homeomorphic to unit interval ${\Bbb I}$. The notion of unit square $\square_{\cal E^{2}_{\rm T}}$ has been also introduced and some facts about it have been proved.

#### MML Identifier: TOPREAL1

The terminology and notation used in this paper have been introduced in the following articles [15] [18] [2] [3] [16] [11] [1] [19] [6] [7] [8] [13] [4] [17] [12] [10] [5] [9] [14]

Contents (PDF format)

#### Bibliography

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