# A base of a funcoid which is not a filter base

The converse of this theorem does not hold.

Counterexample: Take $S = \mathrm{up}\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$. We know that $S$ is not a filter base. But it is trivial to prove that $S$ is a base of the funcoid $\mathrm{id}^{\mathsf{FCD}}_{\Omega}$.