Volume 8, 1996

University of Bialystok

Copyright (c) 1996 Association of Mizar Users

**Artur Kornilowicz**- Institute of Mathematics, Warsaw University, Bialystok

- 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.

- Preliminaries
- The properties of nets
- On the inf and sup operation
- Meet-continuous lattices

- [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.

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