# Chain-meet-closed sets (Solved)

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.