Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003
Association of Mizar Users
Morphisms Into Chains. Part I
-
Artur Kornilowicz
-
University of Bialystok
Summary.
-
This work is the continuation of formalization of [10].
Items from 2.1 to 2.8 of Chapter 4 are proved.
The terminology and notation used in this paper have been
introduced in the following articles
[13]
[7]
[17]
[14]
[4]
[15]
[16]
[1]
[18]
[20]
[19]
[5]
[6]
[2]
[12]
[21]
[3]
[8]
[11]
[9]
-
Preliminaries
-
Main Part
Bibliography
- [1]
Grzegorz Bancerek.
Complete lattices.
Journal of Formalized Mathematics,
4, 1992.
- [2]
Grzegorz Bancerek.
Bounds in posets and relational substructures.
Journal of Formalized Mathematics,
8, 1996.
- [3]
Grzegorz Bancerek.
Directed sets, nets, ideals, filters, and maps.
Journal of Formalized Mathematics,
8, 1996.
- [4]
Jozef Bialas.
Group and field definitions.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
- [8]
Czeslaw Bylinski.
Galois connections.
Journal of Formalized Mathematics,
8, 1996.
- [9]
Marek Dudzicz.
Representation theorem for finite distributive lattices.
Journal of Formalized Mathematics,
12, 2000.
- [10]
G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott.
\em A Compendium of Continuous Lattices.
Springer-Verlag, Berlin, Heidelberg, New York, 1980.
- [11]
Adam Grabowski.
Auxiliary and approximating relations.
Journal of Formalized Mathematics,
8, 1996.
- [12]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
Journal of Formalized Mathematics,
8, 1996.
- [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [14]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [15]
Wojciech A. Trybulec.
Partially ordered sets.
Journal of Formalized Mathematics,
1, 1989.
- [16]
Wojciech A. Trybulec and Grzegorz Bancerek.
Kuratowski - Zorn lemma.
Journal of Formalized Mathematics,
1, 1989.
- [17]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [18]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [19]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
- [20]
Edmund Woronowicz and Anna Zalewska.
Properties of binary relations.
Journal of Formalized Mathematics,
1, 1989.
- [21]
Mariusz Zynel and Czeslaw Bylinski.
Properties of relational structures, posets, lattices and maps.
Journal of Formalized Mathematics,
8, 1996.
Received February 6, 2003
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