Volume 12, 2000

University of Bialystok

Copyright (c) 2000 Association of Mizar Users

**Robert Milewski**- University of Bialystok

- 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.

Contents (PDF format)

- [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.

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