# Atomicity of the poset of multifuncoids

 Importance: Medium ✭✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: multifuncoid
 Posted by: porton on: February 12th, 2012
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.