Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000
Association of Mizar Users
Some Properties of Cells and Gauges
-
Adam Grabowski
-
University of Bialystok
-
Artur Kornilowicz
-
University of Bialystok
-
Andrzej Trybulec
-
University of Bialystok
This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102.
The terminology and notation used in this paper have been
introduced in the following articles
[24]
[27]
[2]
[12]
[26]
[25]
[1]
[4]
[13]
[28]
[17]
[6]
[23]
[3]
[22]
[9]
[10]
[5]
[14]
[11]
[20]
[7]
[21]
[19]
[8]
[15]
[18]
[16]
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.
Countable sets and Hessenberg's theorem.
Journal of Formalized Mathematics,
2, 1990.
- [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 from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Czeslaw Bylinski.
Gauges.
Journal of Formalized Mathematics,
11, 1999.
- [8]
Czeslaw Bylinski and Piotr Rudnicki.
Bounding boxes for compact sets in $\calE^2$.
Journal of Formalized Mathematics,
9, 1997.
- [9]
Agata Darmochwal.
Compact spaces.
Journal of Formalized Mathematics,
1, 1989.
- [10]
Agata Darmochwal.
The Euclidean space.
Journal of Formalized Mathematics,
3, 1991.
- [11]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Simple closed curves.
Journal of Formalized Mathematics,
3, 1991.
- [12]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
- [13]
Katarzyna Jankowska.
Matrices. Abelian group of matrices.
Journal of Formalized Mathematics,
3, 1991.
- [14]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
Journal of Formalized Mathematics,
2, 1990.
- [15]
Artur Kornilowicz.
Properties of left and right components.
Journal of Formalized Mathematics,
11, 1999.
- [16]
Artur Kornilowicz, Robert Milewski, Adam Naumowicz, and Andrzej Trybulec.
Gauges and cages. Part I.
Journal of Formalized Mathematics,
12, 2000.
- [17]
Jaroslaw Kotowicz.
Convergent real sequences. Upper and lower bound of sets of real numbers.
Journal of Formalized Mathematics,
1, 1989.
- [18]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
Journal of Formalized Mathematics,
1, 1989.
- [19]
Yatsuka Nakamura and Czeslaw Bylinski.
Extremal properties of vertices on special polygons, part I.
Journal of Formalized Mathematics,
6, 1994.
- [20]
Yatsuka Nakamura and Andrzej Trybulec.
Decomposing a Go-Board into cells.
Journal of Formalized Mathematics,
7, 1995.
- [21]
Yatsuka Nakamura, Andrzej Trybulec, and Czeslaw Bylinski.
Bounded domains and unbounded domains.
Journal of Formalized Mathematics,
11, 1999.
- [22]
Beata Padlewska.
Connected spaces.
Journal of Formalized Mathematics,
1, 1989.
- [23]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
- [24]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [25]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
Journal of Formalized Mathematics,
1, 1989.
- [26]
Michal J. Trybulec.
Integers.
Journal of Formalized Mathematics,
2, 1990.
- [27]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [28]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received October 13, 2000
[
Download a postscript version,
MML identifier index,
Mizar home page]