Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Partially Ordered Sets

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

In the beginning of this article we define the choice function of
a nonempty set family that does not contain $\emptyset$ as introduced in
[6, pages 8889].
We define order of a
set as a relation being reflexive, antisymmetric and transitive in the set,
partially ordered set as structure nonempty set and order of the set,
chains, lower and upper cone of a subset, initial segments of element and
subset of partially ordered set.
Some theorems that belong rather to [5]
or [12] are proved.
The terminology and notation used in this paper have been
introduced in the following articles
[8]
[5]
[9]
[10]
[12]
[2]
[11]
[4]
[3]
[1]
[7]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The well ordering relations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Kazimierz Kuratowski.
\em Wstep do teorii mnogosci i topologii.
PWN, War\sza\wa, 1977.
 [7]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [9]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Edmund Woronowicz and Anna Zalewska.
Properties of binary relations.
Journal of Formalized Mathematics,
1, 1989.
Received August 30, 1989
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