Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

The Lawson Topology


Grzegorz Bancerek
University of Bialystok

Summary.

The article includes definitions, lemmas and theorems 1.1-1.7, 1.9, 1.10 presented in Chapter III of [11, pp. 142-146].

This work has been partially supported by KBN grant 8 T11C 018 12 and NATO CRG 951368 grant.

MML Identifier: WAYBEL19

The terminology and notation used in this paper have been introduced in the following articles [19] [8] [24] [16] [25] [6] [10] [7] [23] [1] [17] [20] [9] [2] [3] [12] [18] [13] [14] [21] [4] [15] [22] [5]

Contents (PDF format)

  1. Lower Topology
  2. Refinements Revisited
  3. Lawson Topology

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] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[5] Grzegorz Bancerek. Bases and refinements of topologies. Journal of Formalized Mathematics, 10, 1998.
[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. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
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[10] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[11] 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.
[12] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[13] Artur Kornilowicz. Cartesian products of relations and relational structures. Journal of Formalized Mathematics, 8, 1996.
[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] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[19] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[20] Andrzej Trybulec. A Borsuk theorem on homotopy types. Journal of Formalized Mathematics, 3, 1991.
[21] Andrzej Trybulec. Moore-Smith convergence. Journal of Formalized Mathematics, 8, 1996.
[22] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.
[23] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[24] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[25] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received June 21, 1998

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