Volume 13, 2001

University of Bialystok

Copyright (c) 2001 Association of Mizar Users

**Grzegorz Bancerek**- University of Bialystok, Shinshu University, Nagano

- In the paper, we investigate the duality of categories of complete lattices and maps preserving suprema or infima according to [15, p. 179-183; 1.1-1.12]. The duality is based on the concept of the Galois connection.

- Infs-preserving and Sups-preserving Maps
- Scott Continuous Maps and Continuous Lattices
- Duality of Subcategories of {\it INF} and {\it SUP}
- Compact Preserving Maps and Sup-semilattices Morphisms

- [1]
Grzegorz Bancerek.
The well ordering relations.
*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 ``way-below'' relation.
*Journal of Formalized Mathematics*, 8, 1996. - [6]
Grzegorz Bancerek.
Bases and refinements of topologies.
*Journal of Formalized Mathematics*, 10, 1998. - [7]
Grzegorz Bancerek.
Categorial background for duality theory.
*Journal of Formalized Mathematics*, 13, 2001. - [8]
Grzegorz Bancerek.
Miscellaneous facts about functors.
*Journal of Formalized Mathematics*, 13, 2001. - [9]
Czeslaw Bylinski.
Binary operations.
*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.
Galois connections.
*Journal of Formalized Mathematics*, 8, 1996. - [14]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [15] 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.
- [16]
Jaroslaw Gryko.
Injective spaces.
*Journal of Formalized Mathematics*, 10, 1998. - [17]
Beata Madras.
On the concept of the triangulation.
*Journal of Formalized Mathematics*, 7, 1995. - [18]
Robert Milewski.
Algebraic lattices.
*Journal of Formalized Mathematics*, 8, 1996. - [19]
Michal Muzalewski.
Categories of groups.
*Journal of Formalized Mathematics*, 3, 1991. - [20]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [22]
Andrzej Trybulec.
A Borsuk theorem on homotopy types.
*Journal of Formalized Mathematics*, 3, 1991. - [23]
Andrzej Trybulec.
Categories without uniqueness of \rm cod and \rm dom.
*Journal of Formalized Mathematics*, 7, 1995. - [24]
Andrzej Trybulec.
Examples of category structures.
*Journal of Formalized Mathematics*, 8, 1996. - [25]
Andrzej Trybulec.
Functors for alternative categories.
*Journal of Formalized Mathematics*, 8, 1996. - [26]
Andrzej Trybulec.
Scott topology.
*Journal of Formalized Mathematics*, 9, 1997. - [27]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [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. - [32]
Mariusz Zynel and Adam Guzowski.
\Tzero\ topological spaces.
*Journal of Formalized Mathematics*, 6, 1994.

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