# A counterexample: Funcoid corresponding to outer reloid

I found a counter-example to the following conjecture.

Conjecture $(\mathsf{FCD}) (\mathsf{RLD})_{\mathrm{out}} f = f$ for every funcoid $f$.

The counterexample is $f = {(=)}|_{\Omega}$ where $\Omega$ is the Fréchet filter.

See Algebraic General Topology and in particular Funcoids and Reloids online article, the section Some counter-examples for this counterexample.