Importance: Medium ✭✭
 Author(s): Porton, Victor
 Subject: Unsorted
 Keywords: chain complete lattice filter bases filters linear order total order
 Posted by: porton on: December 12th, 2009
 Solved by: Joel David Hamkins

Let is a complete lattice. I will call a filter base a nonempty subset of such that .

Definition   A subset of a complete lattice is chain-meet-closed iff for every non-empty chain we have .
Conjecture   A subset of a complete lattice is chain-meet-closed iff for every filter base we have .

The answer is yes. A proof is present in this online article.

## Bibliography

*Victor Porton. Chain-meet-closed sets on complete lattices

* indicates original appearance(s) of problem.