Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

Basic Notions and Properties of Orthoposets


Markus Moschner
Saarland University
This paper was worked out while the author was visiting the University of Bia{\l}ystok in autumn 2002.

Summary.

Orthoposets are defined. The approach is the standard one via order relation similar to common text books on algebra like [9].

This work has been partially supported by the CALCULEMUS project (FP5 grant HPRN-CT-2000-00102).

MML Identifier: OPOSET_1

The terminology and notation used in this paper have been introduced in the following articles [12] [14] [6] [3] [15] [17] [4] [16] [5] [13] [10] [8] [2] [7] [1] [11]

Contents (PDF format)

  1. General Notions and Properties
  2. Basic Poset Notions

Bibliography

[1] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[2] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[8] Adam Grabowski. Robbins algebras vs. Boolean algebras. Journal of Formalized Mathematics, 13, 2001.
[9] George Gr\"atzer. \em General Lattice Theory. Academic Press, New York, 1978.
[10] Michal Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Journal of Formalized Mathematics, 2, 1990.
[11] Krzysztof Retel. The class of series --- parallel graphs. Journal of Formalized Mathematics, 14, 2002.
[12] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[13] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[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.
[16] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[17] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

Received February 11, 2003

[ Download a postscript version, MML identifier index, Mizar home page]