![](/files/happy5.png)
Let be an indexed family of sets.
Products are for
.
Hyperfuncoids are filters on the lattice
of all finite unions of products.
Problem Is
a bijection from hyperfuncoids
to:
![$ \bigcap^{\mathsf{\tmop{FCD}}} $](/files/tex/3c8ed688fbcae181a7b030c7071347137615d338.png)
![$ \mathfrak{F} \Gamma $](/files/tex/2d4cbeff4993cf10008cbe69e72409840d1b2201.png)
- \item prestaroids on
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
If yes, is defining the inverse bijection? If not, characterize the image of the function
defined on
.
Consider also the variant of this problem with the set replaced with the set
of complements of elements of the set
.
It's used notation from Algebraic General Topology draft book
Bibliography
* indicates original appearance(s) of problem.