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

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[3] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.

[5] Leszek Borys. Paracompact and metrizable spaces. Journal of Formalized Mathematics, 3, 1991.

[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[7] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[8] Agata Darmochwal. Families of subsets, subspaces and mappings in topological spaces. Journal of Formalized Mathematics, 1, 1989.

[9] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.

[10] Agata Darmochwal and Yatsuka Nakamura. Metric spaces as topological spaces --- fundamental concepts. Journal of Formalized Mathematics, 3, 1991.

[11] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

[12] Stanislawa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Journal of Formalized Mathematics, 2, 1990.

[13] Beata Padlewska. Locally connected spaces. Journal of Formalized Mathematics, 2, 1990.

[14] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[16] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[17] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.

[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[19] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.