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


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