Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

## The Properties of Product of Relational Structures

Artur Kornilowicz
University of Bialystok

### Summary.

This work contains useful facts about the product of relational structures. It continues the formalization of [7].

This work has been supported by KBN Grant 8 T11C 018 12.

#### MML Identifier: YELLOW10

The terminology and notation used in this paper have been introduced in the following articles [13] [5] [14] [16] [1] [2] [3] [6] [8] [9] [10] [4] [11] [12] [15]

#### Contents (PDF format)

1. On the Elements of Product of Relational Structures
2. On the Subsets of Product of Relational Structures
3. On the Products of Relational Structures

#### 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] Grzegorz Bancerek. The way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[5] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[7] 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.
[8] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.
[9] Artur Kornilowicz. Definitions and properties of the join and meet of subsets. Journal of Formalized Mathematics, 8, 1996.
[10] Artur Kornilowicz. Meet -- continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[11] Beata Madras. Irreducible and prime elements. Journal of Formalized Mathematics, 8, 1996.
[12] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[13] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[14] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.
[16] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.

Received March 27, 1998

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