Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

Algebraic and Arithmetic Lattices. Part I


Robert Milewski
Warsaw University, Bialystok

Summary.

We formalize [10, pp. 87-89].

This work was partially supported by KBN Grant 8 T11C 018 12.

MML Identifier: WAYBEL13

The terminology and notation used in this paper have been introduced in the following articles [15] [7] [18] [13] [9] [19] [17] [5] [6] [14] [16] [1] [2] [11] [20] [3] [8] [4] [12]

Contents (PDF format)

  1. Preliminaries
  2. Algebraic and Arithmetic Lattices
  3. Maps

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] Grzegorz Bancerek. The ``way-below'' relation. 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. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[9] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[10] 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.
[11] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[12] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[13] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[14] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[17] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[19] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[20] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received March 4, 1997

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