Volume 13, 2001

University of Bialystok

Copyright (c) 2001 Association of Mizar Users

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

- Formalization of [14], chapter III, section 3 (3.4-3.6).

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.
Prime ideals and filters.
*Journal of Formalized Mathematics*, 8, 1996. - [5]
Grzegorz Bancerek.
Bases and refinements of topologies.
*Journal of Formalized Mathematics*, 10, 1998. - [6]
Grzegorz Bancerek.
The Lawson topology.
*Journal of Formalized Mathematics*, 10, 1998. - [7]
Grzegorz Bancerek, Noboru Endou, and Yuji Sakai.
On the characterizations of compactness.
*Journal of Formalized Mathematics*, 13, 2001. - [8]
Jozef Bialas and Yatsuka Nakamura.
Dyadic numbers and T$_4$ topological spaces.
*Journal of Formalized Mathematics*, 7, 1995. - [9]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Agata Darmochwal.
Compact spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [14] 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.
- [15]
Adam Grabowski and Robert Milewski.
Boolean posets, posets under inclusion and products of relational structures.
*Journal of Formalized Mathematics*, 8, 1996. - [16]
Zbigniew Karno.
Maximal discrete subspaces of almost discrete topological spaces.
*Journal of Formalized Mathematics*, 5, 1993. - [17]
Artur Kornilowicz.
On the topological properties of meet-continuous lattices.
*Journal of Formalized Mathematics*, 8, 1996. - [18]
Beata Padlewska.
Families of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [20]
Alexander Yu. Shibakov and Andrzej Trybulec.
The Cantor set.
*Journal of Formalized Mathematics*, 7, 1995. - [21]
Bartlomiej Skorulski.
Lim-inf convergence.
*Journal of Formalized Mathematics*, 12, 2000. - [22]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [23]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Andrzej Trybulec.
Moore-Smith convergence.
*Journal of Formalized Mathematics*, 8, 1996. - [25]
Andrzej Trybulec.
Scott topology.
*Journal of Formalized Mathematics*, 9, 1997. - [26]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [27]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [28]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [29]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [30]
Mariusz Zynel and Czeslaw Bylinski.
Properties of relational structures, posets, lattices and maps.
*Journal of Formalized Mathematics*, 8, 1996.

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