I found a counter-example to the following conjecture.

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

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

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

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