Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

Bases of Continuous Lattices


Robert Milewski
University of Bialystok

Summary.

The article is a Mizar formalization of [13, 168-169]. We show definition and fundamental theorems from theory of basis of continuous lattices.

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

MML Identifier: WAYBEL23

The terminology and notation used in this paper have been introduced in the following articles [19] [21] [16] [22] [8] [9] [10] [12] [2] [3] [1] [17] [20] [18] [4] [5] [14] [23] [6] [11] [7] [15]

Contents (PDF format)

  1. Preliminaries
  2. Relational Subsets
  3. About Bases of Continuous Lattices

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[5] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[6] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[7] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[8] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[12] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[13] 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.
[14] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[15] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[16] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[19] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[20] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[23] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received November 28, 1998


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