Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997
Association of Mizar Users
The Ordering of Points on a Curve. Part II
-
Adam Grabowski
-
University of Bialystok
-
This paper was written while the author visited the Shinshu
University in the winter of 1997.
-
Yatsuka Nakamura
-
Shinshu University, Nagano
Summary.
-
The proof of the Jordan Curve Theorem according to
[11] is continued. The notions of the first
and last point of a oriented arc are introduced as well
as ordering of points on a curve in $\calE^2_T$.
The terminology and notation used in this paper have been
introduced in the following articles
[12]
[14]
[1]
[15]
[2]
[3]
[4]
[7]
[13]
[9]
[8]
[10]
[5]
[6]
-
First and last point of a curve
-
The ordering of points on a curve
-
Some properties of the ordering of points on a curve
Bibliography
- [1]
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The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
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- [2]
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Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
- [3]
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Journal of Formalized Mathematics,
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- [4]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
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- [5]
Agata Darmochwal.
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Journal of Formalized Mathematics,
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- [6]
Agata Darmochwal.
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Metric spaces as topological spaces --- fundamental concepts.
Journal of Formalized Mathematics,
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- [8]
Agata Darmochwal and Yatsuka Nakamura.
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Journal of Formalized Mathematics,
3, 1991.
- [9]
Yatsuka Nakamura and Roman Matuszewski.
Reconstructions of special sequences.
Journal of Formalized Mathematics,
8, 1996.
- [10]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
- [11]
Yukio Takeuchi and Yatsuka Nakamura.
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Technical Report 19804, Dept. of Information Eng., Shinshu
University, 500 Wakasato, Nagano city, Japan, April 1980.
- [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 September 10, 1997
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