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

Bounds in Posets and Relational Substructures


Grzegorz Bancerek
Institute of Mathematics, Polish Academy of Sciences

Summary.

Notation and facts necessary to start with the formalization of continuous lattices according to [4] are introduced.

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

MML Identifier: YELLOW_0

The terminology and notation used in this paper have been introduced in the following articles [6] [2] [8] [10] [9] [3] [5] [11] [7] [1]

Contents (PDF format)

  1. Reexamination of poset concepts
  2. Least upper and greatest lower bounds
  3. Relational substructures

Bibliography

[1] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[2] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[3] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[4] 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.
[5] Krzysztof Hryniewiecki. Relations of tolerance. Journal of Formalized Mathematics, 2, 1990.
[6] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[7] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[9] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[10] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.
[11] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received September 10, 1996


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