Definition A set of binary relations is a base of a funcoid
when all elements of
are above
and
.
It was easy to show:
Proposition A set of binary relations is a base of a funcoid iff it is a base of
.
Today I’ve proved the following important theorem:
Theorem If is a filter base on the set of funcoids then
is a base of
.
The proof is currently located in this PDF file.
It is yet unknown whether the converse theorem holds, that is whether every base of a funcoid is a filter base on the set of funcoids.
One comment