# 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