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

Algebraic Lattices


Robert Milewski
Warsaw University, Bialystok

MML Identifier: WAYBEL_8

The terminology and notation used in this paper have been introduced in the following articles [16] [8] [18] [14] [10] [19] [17] [7] [1] [15] [2] [3] [12] [20] [4] [9] [6] [11] [13] [5]

Contents (PDF format)

  1. The Subset of All Compact Elements
  2. Algebraic Lattices
  3. Arithmetic Lattices
  4. Boolean Posets as Algebraic Lattices

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] Grzegorz Bancerek. Prime ideals and filters. Journal of Formalized Mathematics, 8, 1996.
[6] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[7] Czeslaw Bylinski. Functions and their basic properties. 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] Adam Grabowski. Auxiliary and approximating relations. Journal of Formalized Mathematics, 8, 1996.
[12] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[13] Beata Madras. Irreducible and prime elements. Journal of Formalized Mathematics, 8, 1996.
[14] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[15] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[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 December 1, 1996

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