![](/files/happy5.png)
Conjecture The poset of completary multifuncoids of the form
is for every sets
and
:
![$ (\mathscr{P}\mho)^n $](/files/tex/02023fd10859168be6be125aa8d3912904f57a27.png)
![$ \mho $](/files/tex/8a60ffddf5f015b5658f273c0698af378fdebbde.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
- \item atomic; \item atomistic.
See below for definition of all concepts and symbols used to in this conjecture.
Refer to this Web site for the theory which I now attempt to generalize.
Definition Let
is a family of join-semilattice. A completary multifuncoid of the form
is an
such that we have that:
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
![$ f \in \mathscr{P} \prod \mathfrak{A} $](/files/tex/549eb9137ca23d96fcd29b48666a1612a8a5818b.png)
- \item
![$ L_0 \cup L_1 \in f \Leftrightarrow \exists c \in \left\{ 0, 1 \right\}^n : \left( \lambda i \in n : L_{c \left( i_{} \right)} i \right) \in f $](/files/tex/3f6a3cca43a2afc884cf51e4abb225b148a02c79.png)
![$ L_0, L_1 \in \prod \mathfrak{A} $](/files/tex/e2d9708b1dadb9f03d9703d4459f860fdbde1ac1.png)
\item If and
for some
then
.
is a function space over a poset
that is
for
.
Bibliography
* indicates original appearance(s) of problem.