Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

**Grzegorz Bancerek**- University of Bialystok

- The article includes definitions, lemmas and theorems 1.1-1.7, 1.9, 1.10 presented in Chapter III of [11, pp. 142-146].

This work has been partially supported by KBN grant 8 T11C 018 12 and NATO CRG 951368 grant.

- Lower Topology
- Refinements Revisited
- Lawson Topology

- [1]
Grzegorz Bancerek.
Complete lattices.
*Journal of Formalized Mathematics*, 4, 1992. - [2]
Grzegorz Bancerek.
Bounds in posets and relational substructures.
*Journal of Formalized Mathematics*, 8, 1996. - [3]
Grzegorz Bancerek.
Directed sets, nets, ideals, filters, and maps.
*Journal of Formalized Mathematics*, 8, 1996. - [4]
Grzegorz Bancerek.
The ``way-below'' relation.
*Journal of Formalized Mathematics*, 8, 1996. - [5]
Grzegorz Bancerek.
Bases and refinements of topologies.
*Journal of Formalized Mathematics*, 10, 1998. - [6]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Agata Darmochwal.
Compact spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [11] 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.
- [12]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
*Journal of Formalized Mathematics*, 8, 1996. - [13]
Artur Kornilowicz.
Cartesian products of relations and relational structures.
*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 meet-continuous 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]
Andrzej Trybulec.
A Borsuk theorem on homotopy types.
*Journal of Formalized Mathematics*, 3, 1991. - [21]
Andrzej Trybulec.
Moore-Smith convergence.
*Journal of Formalized Mathematics*, 8, 1996. - [22]
Andrzej Trybulec.
Scott topology.
*Journal of Formalized Mathematics*, 9, 1997. - [23]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [25]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

[ Download a postscript version, MML identifier index, Mizar home page]