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

Meet -- Continuous Lattices


Artur Kornilowicz
Institute of Mathematics, Warsaw University, Bialystok

Summary.

The aim of this work is the formalization of Chapter 0 Section 4 of [11]. In this paper the definition of meet-continuous lattices is introduced. Theorem 4.2 and Remark 4.3 are proved.

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

MML Identifier: WAYBEL_2

The terminology and notation used in this paper have been introduced in the following articles [18] [8] [21] [22] [19] [5] [14] [10] [7] [6] [17] [4] [20] [12] [1] [2] [3] [13] [23] [9] [15] [16]

Contents (PDF format)

  1. Preliminaries
  2. The properties of nets
  3. On the inf and sup operation
  4. Meet-continuous lattices

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] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[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. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[10] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[11] 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.
[12] Adam Grabowski. On the category of posets. Journal of Formalized Mathematics, 8, 1996.
[13] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[14] Krzysztof Hryniewiecki. Relations of tolerance. Journal of Formalized Mathematics, 2, 1990.
[15] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.
[16] Artur Kornilowicz. Definitions and properties of the join and meet of subsets. Journal of Formalized Mathematics, 8, 1996.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[19] Andrzej Trybulec and Agata Darmochwal. Boolean domains. Journal of Formalized Mathematics, 1, 1989.
[20] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[23] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received October 10, 1996

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