Today I proved the following conjecture:
If a reloid is both complete and co-complete it is discrete.
The proof was easily constructed by me shortly after I noticed an obvious but not noticed before proposition:
Proposition A reloid $latex f$ is complete iff there exists a function $latex G : \mho \rightarrow \mathfrak{F}$ such that
$latex f = \bigcup^{\mathsf{RLD}} \{ \{\alpha\} \times^{\mathsf{RLD}} G (\alpha) | \alpha \in \mho \}$.
Note that a similar theorem holds for funcoids.
See the online article for details about funcoids and reloids.