Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

Weights of Continuous Lattices


Robert Milewski
University of Bialystok

Summary.

This work is a continuation of formalization of [16]. Theorems from Chapter III, Section 4, pp. 170-171 are proved.

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

MML Identifier: WAYBEL31

The terminology and notation used in this paper have been introduced in the following articles [24] [12] [28] [21] [15] [30] [27] [29] [10] [11] [9] [13] [2] [1] [22] [23] [26] [3] [4] [17] [31] [7] [5] [14] [6] [19] [18] [25] [8] [20]

Contents (PDF format)

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. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[4] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[5] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[6] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[7] Grzegorz Bancerek. Bases and refinements of topologies. Journal of Formalized Mathematics, 10, 1998.
[8] Grzegorz Bancerek. The Lawson topology. Journal of Formalized Mathematics, 10, 1998.
[9] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[12] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[13] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[14] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[15] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[16] 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.
[17] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[18] Artur Kornilowicz. On the topological properties of meet-continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[19] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[20] Robert Milewski. Bases of continuous lattices. Journal of Formalized Mathematics, 10, 1998.
[21] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[22] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[23] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[24] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[25] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.
[26] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[27] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[28] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[29] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[30] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[31] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received January 6, 2000


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