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

Lawson Topology in Continuous Lattices


Grzegorz Bancerek
University of Bialystok

Summary.

The article completes Mizar formalization of Section 1 of Chapter III of [11, pp. 145-147].

Partially supported by NATO Grant CRG 951368, NSERC OGP 9207 grant and KBN grant 8 T11C 018 12.

MML Identifier: WAYBEL21

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

Contents (PDF format)

  1. Semilattice Homomorphism and Inheritance
  2. Nets and Limits
  3. Lawson Topology Revisited

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] Grzegorz Bancerek. The Lawson topology. Journal of Formalized Mathematics, 10, 1998.
[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[9] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.
[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. On the category of posets. Journal of Formalized Mathematics, 8, 1996.
[13] Adam Grabowski. Scott-continuous functions. Journal of Formalized Mathematics, 10, 1998.
[14] Artur Kornilowicz. On the topological properties of meet-continuous lattices. Journal of Formalized Mathematics, 8, 1996.
[15] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Andrzej Trybulec. Moore-Smith convergence. Journal of Formalized Mathematics, 8, 1996.
[18] Andrzej Trybulec. Scott topology. Journal of Formalized Mathematics, 9, 1997.
[19] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[20] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[22] Mariusz Zynel and Czeslaw Bylinski. Properties of relational structures, posets, lattices and maps. Journal of Formalized Mathematics, 8, 1996.

Received July 12, 1998

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