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filter
Join of oblique products ★★
Author(s): Porton
Conjecture
for every filter objects
,
.
![$ \left( \mathcal{A} \ltimes \mathcal{B} \right) \cup \left( \mathcal{A} \rtimes \mathcal{B} \right) = \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} $](/files/tex/985106da22b932d63d15946e484e9de0ba9c261d.png)
![$ \mathcal{A} $](/files/tex/3abde4ab7e21fe6fad91d0a03ad306c2c82659d9.png)
![$ \mathcal{B} $](/files/tex/cca7b496bd14e6acf10041305acbd75cd720f9b3.png)
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
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