**Conjecture**The poset of 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**A free star on a join-semilattice with least element 0 is a set such that and

**Definition**Let be a family of posets, ( has the order of function space of posets), , . Then

**Definition**Let is a family of posets. A multidimensional funcoid (or multifuncoid for short) of the form is an such that we have that:

- \item is a free star for every , .

\item is an upper set.

is a function space over a poset that is for .

## Bibliography

* indicates original appearance(s) of problem.