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

## Galois Connections

Czeslaw Bylinski
Warsaw University, Bialystok

### Summary.

The paper is the Mizar encoding of the chapter 0 section 3 of [9] In the paper the following concept are defined: Galois connections, Heyting algebras, and Boolean algebras.

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

#### MML Identifier: WAYBEL_1

The terminology and notation used in this paper have been introduced in the following articles [14] [8] [16] [5] [7] [6] [13] [15] [1] [2] [10] [3] [12] [11] [4] [17]

#### Contents (PDF format)

1. Preliminaries
2. Galois Connections
3. Heyting Algebra

#### Bibliography

[1] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[2] Grzegorz Bancerek. Quantales. Journal of Formalized Mathematics, 6, 1994.
[3] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[4] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[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] 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.
[10] Adam Grabowski. On the category of posets. Journal of Formalized Mathematics, 8, 1996.
[11] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[12] Michal Muzalewski. Categories of groups. Journal of Formalized Mathematics, 3, 1991.
[13] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[14] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[15] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[16] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[17] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received September 25, 1996

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