Volume 11, 1999

University of Bialystok

Copyright (c) 1999 Association of Mizar Users

**Grzegorz Bancerek**- University of Bialystok

- Formalization of [20, pp. 128-130], chapter II, section 4 (4.1 - 4.9).

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

- [1]
Grzegorz Bancerek.
Curried and uncurried functions.
*Journal of Formalized Mathematics*, 2, 1990. - [2]
Grzegorz Bancerek.
K\"onig's theorem.
*Journal of Formalized Mathematics*, 2, 1990. - [3]
Grzegorz Bancerek.
Complete lattices.
*Journal of Formalized Mathematics*, 4, 1992. - [4]
Grzegorz Bancerek.
Quantales.
*Journal of Formalized Mathematics*, 6, 1994. - [5]
Grzegorz Bancerek.
Bounds in posets and relational substructures.
*Journal of Formalized Mathematics*, 8, 1996. - [6]
Grzegorz Bancerek.
Directed sets, nets, ideals, filters, and maps.
*Journal of Formalized Mathematics*, 8, 1996. - [7]
Grzegorz Bancerek.
The ``way-below'' relation.
*Journal of Formalized Mathematics*, 8, 1996. - [8]
Grzegorz Bancerek.
Bases and refinements of topologies.
*Journal of Formalized Mathematics*, 10, 1998. - [9]
Grzegorz Bancerek.
Retracts and inheritance.
*Journal of Formalized Mathematics*, 11, 1999. - [10]
Jozef Bialas.
Group and field definitions.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Jozef Bialas and Yatsuka Nakamura.
Dyadic numbers and T$_4$ topological spaces.
*Journal of Formalized Mathematics*, 7, 1995. - [12]
Czeslaw Bylinski.
Basic functions and operations on functions.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [16]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [17]
Czeslaw Bylinski.
Galois connections.
*Journal of Formalized Mathematics*, 8, 1996. - [18]
Agata Darmochwal.
Families of subsets, subspaces and mappings in topological spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [20] 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.
- [21]
Adam Grabowski.
Scott-continuous functions. Part II.
*Journal of Formalized Mathematics*, 11, 1999. - [22]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
*Journal of Formalized Mathematics*, 8, 1996. - [23]
Jaroslaw Gryko.
Injective spaces.
*Journal of Formalized Mathematics*, 10, 1998. - [24]
Zbigniew Karno.
On Kolmogorov topological spaces.
*Journal of Formalized Mathematics*, 6, 1994. - [25]
Artur Kornilowicz.
On the topological properties of meet-continuous lattices.
*Journal of Formalized Mathematics*, 8, 1996. - [26]
Artur Kornilowicz and Jaroslaw Gryko.
Injective spaces. Part II.
*Journal of Formalized Mathematics*, 11, 1999. - [27]
Beata Madras.
Product of family of universal algebras.
*Journal of Formalized Mathematics*, 5, 1993. - [28]
Beata Madras.
Products of many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [29]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Preliminaries to circuits, I.
*Journal of Formalized Mathematics*, 6, 1994. - [30]
Andrzej Nedzusiak.
$\sigma$-fields and probability.
*Journal of Formalized Mathematics*, 1, 1989. - [31]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [32]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [33]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [34]
Andrzej Trybulec.
A Borsuk theorem on homotopy types.
*Journal of Formalized Mathematics*, 3, 1991. - [35]
Andrzej Trybulec.
Many-sorted sets.
*Journal of Formalized Mathematics*, 5, 1993. - [36]
Andrzej Trybulec.
Scott topology.
*Journal of Formalized Mathematics*, 9, 1997. - [37]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [38]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [39]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [40]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [41]
Mariusz Zynel and Czeslaw Bylinski.
Properties of relational structures, posets, lattices and maps.
*Journal of Formalized Mathematics*, 8, 1996. - [42]
Mariusz Zynel and Adam Guzowski.
\Tzero\ topological spaces.
*Journal of Formalized Mathematics*, 6, 1994.

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