Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992
Association of Mizar Users
Connectedness Conditions Using Polygonal Arcs

Yatsuka Nakamura

Shinshu University, Nagano

Jaroslaw Kotowicz

Warsaw University, Bialystok

The article was written during my visit at Shinshu University in 1992.
Summary.

A concept of special polygonal arc joining two different points
is defined. Any two points in a ball
can be connected by this kind of arc, and that is also true for any region in
${\cal E}^2_{\rm T}$.
The terminology and notation used in this paper have been
introduced in the following articles
[12]
[14]
[2]
[8]
[1]
[15]
[4]
[3]
[13]
[11]
[10]
[9]
[5]
[6]
[7]
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 and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Agata Darmochwal.
The Euclidean space.
Journal of Formalized Mathematics,
3, 1991.
 [6]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs.
Journal of Formalized Mathematics,
3, 1991.
 [7]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Simple closed curves.
Journal of Formalized Mathematics,
3, 1991.
 [8]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
Journal of Formalized Mathematics,
2, 1990.
 [10]
Beata Padlewska.
Connected spaces.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [13]
Wojciech A. Trybulec.
Pigeon hole principle.
Journal of Formalized Mathematics,
2, 1990.
 [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received August 24, 1992
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