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.III24.C1.
Summary.

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