Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997
Association of Mizar Users
The Scott Topology. Part II

Czeslaw Bylinski

Warsaw University, Bialystok

Piotr Rudnicki

University of Alberta, Edmonton
Summary.

Mizar formalization of pp. 105108 of [10] which continues
[27]. We found a simplification for the proof
of Corollary~1.15,
in the last case, see the proof in the Mizar article for details.
This work was partially supported by NSERC Grant OGP9207
and NATO CRG 951368.
The terminology and notation used in this paper have been
introduced in the following articles
[23]
[7]
[29]
[18]
[9]
[22]
[6]
[28]
[2]
[1]
[20]
[19]
[24]
[21]
[8]
[3]
[11]
[12]
[13]
[25]
[26]
[4]
[14]
[5]
[30]
[16]
[17]
[15]
[27]

Preliminaries

The Scott topology \NotkaDoWaybelXIV
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
Complete lattices.
Journal of Formalized Mathematics,
4, 1992.
 [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 ``waybelow'' relation.
Journal of Formalized Mathematics,
8, 1996.
 [6]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Agata Darmochwal.
Compact spaces.
Journal of Formalized Mathematics,
1, 1989.
 [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.
SpringerVerlag, 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]
Artur Kornilowicz.
Cartesian products of relations and relational structures.
Journal of Formalized Mathematics,
8, 1996.
 [13]
Artur Kornilowicz.
Definitions and properties of the join and meet of subsets.
Journal of Formalized Mathematics,
8, 1996.
 [14]
Artur Kornilowicz.
Meet  continuous lattices.
Journal of Formalized Mathematics,
8, 1996.
 [15]
Artur Kornilowicz.
On the topological properties of meetcontinuous lattices.
Journal of Formalized Mathematics,
8, 1996.
 [16]
Beata Madras.
Irreducible and prime elements.
Journal of Formalized Mathematics,
8, 1996.
 [17]
Robert Milewski.
Algebraic lattices.
Journal of Formalized Mathematics,
8, 1996.
 [18]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [19]
Beata Padlewska.
Locally connected spaces.
Journal of Formalized Mathematics,
2, 1990.
 [20]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
 [21]
Alexander Yu. Shibakov and Andrzej Trybulec.
The Cantor set.
Journal of Formalized Mathematics,
7, 1995.
 [22]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [23]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [24]
Andrzej Trybulec.
A Borsuk theorem on homotopy types.
Journal of Formalized Mathematics,
3, 1991.
 [25]
Andrzej Trybulec.
MooreSmith convergence.
Journal of Formalized Mathematics,
8, 1996.
 [26]
Andrzej Trybulec.
Baire spaces, Sober spaces.
Journal of Formalized Mathematics,
9, 1997.
 [27]
Andrzej Trybulec.
Scott topology.
Journal of Formalized Mathematics,
9, 1997.
 [28]
Wojciech A. Trybulec.
Partially ordered sets.
Journal of Formalized Mathematics,
1, 1989.
 [29]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [30]
Mariusz Zynel.
The equational characterization of continuous lattices.
Journal of Formalized Mathematics,
8, 1996.
Received August 27, 1997
[
Download a postscript version,
MML identifier index,
Mizar home page]