On the Order-consistent Topology of Complete and Uncomplete Lattices

Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

On the Order-consistent Topology of Complete and Uncomplete Lattices

Ewa Gradzka: University of Bialystok

Summary.

This paper is a continuation of the formalisation of [9] pp.~108-109. Order-consistent and upper topologies are defined. The theorem that the Scott and the upper topologies are order-consistent is proved. Remark 1.4 and example 1.5(2) are generalized for proving this theorem.

MML Identifier: WAYBEL32

The terminology and notation used in this paper have been introduced in the following articles [15] [7] [20] [21] [5] [8] [6] [18] [1] [13] [12] [23] [19] [2] [3] [14] [10] [16] [11] [22] [17] [4]

Contents (PDF format)

Acknowledgments

I would like to thank Dr. Grzegorz Bancerek for his help in the preparation of this article.

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Received May 23, 2000

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