I’ve proved today (the proof is surprisingly simple) that a funcoid $latex f$ is complete, if and only if $latex f\circ \bigcup K=\bigcup_{g\in K}(f\circ g)$ for any set $latex K$ of funcoids. Moreover, $latex K$ can be restricted to only principal funcoids without loss of equivalency.
See Algebraic Theory of General Topology.
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