Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

On the Topological Properties of Meet-Continuous Lattices


Artur Kornilowicz
Warsaw University, Bialystok

Summary.

This work is continuation of formalization of [12]. Proposition 4.4 from Chapter 0 is proved.

This work was partially supported by the Office of Naval Research Grant N00014-95-1-1336.

MML Identifier: WAYBEL_9

The terminology and notation used in this paper have been introduced in the following articles [22] [26] [23] [27] [28] [29] [5] [11] [19] [15] [7] [6] [21] [10] [25] [9] [4] [20] [1] [13] [2] [3] [14] [30] [8] [18] [16] [17] [24]

Contents (PDF format)

  1. Preliminaries
  2. The Operations Defined on Nets
  3. The Properties of Topological Spaces
  4. The Cluster Points of Nets
  5. On The Topological Properties of Meet-Continuous Lattices

Bibliography

[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] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
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[13] Adam Grabowski. On the category of posets. Journal of Formalized Mathematics, 8, 1996.
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[16] Artur Kornilowicz. Definitions and properties of the join and meet of subsets. Journal of Formalized Mathematics, 8, 1996.
[17] Artur Kornilowicz. Meet -- continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[18] Michal Muzalewski. Categories of groups. Journal of Formalized Mathematics, 3, 1991.
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[21] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[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] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[26] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[27] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
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[29] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. 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.

Received December 20, 1996


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