Volume 12, 2000

University of Bialystok

Copyright (c) 2000 Association of Mizar Users

**Ewa Gradzka**- University of Bialystok

- This paper is a continuation of the formalisation of [9] pp.~108-109. Order-consistent and upper topologies are defined. The theorem that the Scott and the upper topologies are order-consistent is proved. Remark 1.4 and example 1.5(2) are generalized for proving this theorem.

Contents (PDF format)

- [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.
Bases and refinements of topologies.
*Journal of Formalized Mathematics*, 10, 1998. - [5]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [9] 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.
- [10]
Artur Kornilowicz.
Meet -- continuous lattices.
*Journal of Formalized Mathematics*, 8, 1996. - [11]
Artur Kornilowicz.
On the topological properties of meet-continuous lattices.
*Journal of Formalized Mathematics*, 8, 1996. - [12]
Beata Padlewska.
Locally connected spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [13]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Alexander Yu. Shibakov and Andrzej Trybulec.
The Cantor set.
*Journal of Formalized Mathematics*, 7, 1995. - [15]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [16]
Andrzej Trybulec.
Moore-Smith convergence.
*Journal of Formalized Mathematics*, 8, 1996. - [17]
Andrzej Trybulec.
Scott topology.
*Journal of Formalized Mathematics*, 9, 1997. - [18]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Wojciech A. Trybulec.
Groups.
*Journal of Formalized Mathematics*, 2, 1990. - [20]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Mariusz Zynel and Adam Guzowski.
\Tzero\ topological spaces.
*Journal of Formalized Mathematics*, 6, 1994.

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