
filter
Join of oblique products ★★
Author(s): Porton
Conjecture
for every filter objects
,
.



Keywords: filter; oblique product; reloidal product
Do filters complementive to a given filter form a complete lattice? ★★
Author(s): Porton
Let is a set. A filter (on
)
is by definition a non-empty set of subsets of
such that
. Note that unlike some other authors I do not require
. I will denote
the lattice of all filters (on
) ordered by set inclusion.
Let is some (fixed) filter. Let
. Obviously
is a bounded lattice.
I will call complementive such filters that:
;
is a complemented element of the lattice
.
Conjecture The set of complementive filters ordered by inclusion is a complete lattice.
Keywords: complete lattice; filter
