Partially Ordered Sets

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III-24.C1.

Summary.

In the beginning of this article we define the choice function of a non-empty set family that does not contain $\emptyset$ as introduced in [6, pages 88-89]. We define order of a set as a relation being reflexive, antisymmetric and transitive in the set, partially ordered set as structure non-empty 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.

MML Identifier: ORDERS_1

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.