Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996
Association of Mizar Users
Definitions and Properties of the Join and Meet of Subsets
-
Artur Kornilowicz
-
Institute of Mathematics, Warsaw University, Bialystok
Summary.
-
This paper is the continuation of formalization of [4].
The definitions of meet and join of subsets of relational structures
are introduced. The properties of these notions are proved.
This work was partially supported by
Office of Naval Research Grant N00014-95-1-1336.
The terminology and notation used in this paper have been
introduced in the following articles
[8]
[10]
[7]
[1]
[2]
[9]
[5]
[3]
[6]
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Preliminaries
-
The Join of Subsets
-
The Meet of Subsets
Bibliography
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Complete lattices.
Journal of Formalized Mathematics,
4, 1992.
- [2]
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Journal of Formalized Mathematics,
8, 1996.
- [3]
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- [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]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
Journal of Formalized Mathematics,
8, 1996.
- [6]
Artur Kornilowicz.
Cartesian products of relations and relational structures.
Journal of Formalized Mathematics,
8, 1996.
- [7]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
- [8]
Andrzej Trybulec.
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Journal of Formalized Mathematics,
Axiomatics, 1989.
- [9]
Wojciech A. Trybulec.
Partially ordered sets.
Journal of Formalized Mathematics,
1, 1989.
- [10]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received September 25, 1996
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