Upgrading a completary multifuncoid
Let be a set, be the set of filters on ordered reverse to set-theoretic inclusion, be the set of principal filters on , let be an index set. Consider the filtrator .
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.
Having fixed a filtrator, we define:
- for every .
- If and for some then .
is a function space over a poset that is for .
For finite this problem is equivalent to Upgrading a multifuncoid .
It is not hard to prove this conjecture for the case using the techniques from this my article. But I failed to prove it for and above.
* indicates original appearance(s) of problem.