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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