Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

Filters --- Part I


Grzegorz Bancerek
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

Summary.

Filters of a lattice, maximal filters (ultrafilters), operation to create a filter generating by an element or by a non-empty subset of the lattice are discussed. Besides, there are introduced implicative lattices such that for every two elements there is an element being pseudo-complement of them. Some facts concerning these concepts are presented too, i.e. for any proper filter there exists an ultrafilter consisting it.

MML Identifier: FILTER_0

The terminology and notation used in this paper have been introduced in the following articles [7] [4] [5] [1] [8] [11] [3] [2] [12] [6] [9] [10]

Contents (PDF format)

Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[5] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[6] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[7] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[8] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[9] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[10] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[11] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.
[12] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received July 3, 1990


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