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

Algebraic and Arithmetic Lattices. Part II


Robert Milewski
University of Bialystok

Summary.

The article is a translation of [10, pp. 89-92].

This work has been supported by KBN Grant 8 T11C 018 12.

MML Identifier: WAYBEL15

The terminology and notation used in this paper have been introduced in the following articles [16] [18] [19] [6] [7] [9] [17] [15] [2] [14] [1] [3] [11] [21] [4] [8] [5] [20] [12] [13]

Contents (PDF format)

  1. Preliminaries
  2. Maps Preserving Sup's and Inf's
  3. Atoms Elements
  4. More on the Boolean Lattice

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. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions from a set to a set. 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] Beata Madras. Irreducible and prime elements. Journal of Formalized Mathematics, 8, 1996.
[13] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[14] Michal Muzalewski. Categories of groups. Journal of Formalized Mathematics, 3, 1991.
[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. The equational characterization of continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[21] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received October 29, 1997


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