Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

Cartesian Products of Relations and Relational Structures


Artur Kornilowicz
Institute of Mathematics, Warsaw University, Bialystok

Summary.

In this paper the definitions of cartesian products of relations and relational structures are introduced. Facts about these notions are proved. This work is the continuation of formalization of [8].

This work was partially supported by Office of Naval Research Grant N00014-95-1-1336.

MML Identifier: YELLOW_3

The terminology and notation used in this paper have been introduced in the following articles [9] [7] [12] [13] [15] [14] [5] [10] [6] [1] [11] [2] [3] [4]

Contents (PDF format)

  1. Preliminaries
  2. Properties of Cartesian Products of Relational Structures

Bibliography

[1] Grzegorz Bancerek. Curried and uncurried functions. Journal of Formalized Mathematics, 2, 1990.
[2] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[3] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[4] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[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] 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.
[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[10] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[11] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[12] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[13] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[14] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[15] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

Received September 25, 1996

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