**Conjecture**The poset of completary multifuncoids of the form is for every sets and :

- \item atomic; \item atomistic.

See below for definition of all concepts and symbols used to in this conjecture.

Refer to this Web site for the theory which I now attempt to generalize.

**Definition**Let is a family of join-semilattice. A completary multifuncoid of the form is an such that we have that:

- \item for every .

\item If and for some then .

is a function space over a poset that is for .

## Bibliography

* indicates original appearance(s) of problem.