**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