Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

**Adam Grabowski**- University of Bialystok

- The article is a translation of [10, pp. 112-113].

This work has been supported by KBN Grant 8 T11C 018 12.

- Preliminaries
- Poset of Continuous Maps
- Some Special Nets
- Monotone Maps
- Necessary and Sufficient Conditions of Scott-continuity

- [1]
Grzegorz Bancerek.
The fundamental properties of natural 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 ``way-below'' relation.
*Journal of Formalized Mathematics*, 8, 1996. - [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.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Czeslaw Bylinski.
Some basic properties of 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. Springer-Verlag, Berlin, Heidelberg, New York, 1980.
- [11]
Adam Grabowski.
On the category of posets.
*Journal of Formalized Mathematics*, 8, 1996. - [12]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
*Journal of Formalized Mathematics*, 8, 1996. - [13]
Krzysztof Hryniewiecki.
Relations of tolerance.
*Journal of Formalized Mathematics*, 2, 1990. - [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]
Robert Milewski.
Algebraic lattices.
*Journal of Formalized Mathematics*, 8, 1996. - [17]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [19]
Andrzej Trybulec.
Natural transformations. Discrete categories.
*Journal of Formalized Mathematics*, 3, 1991. - [20]
Andrzej Trybulec.
Scott topology.
*Journal of Formalized Mathematics*, 9, 1997. - [21]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [22]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [25]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [26]
Mariusz Zynel and Czeslaw Bylinski.
Properties of relational structures, posets, lattices and maps.
*Journal of Formalized Mathematics*, 8, 1996.

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