Weights of Continuous Lattices
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.
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
[
Download a postscript version,
MML identifier index,
Mizar home page]