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March 13, 2011 / porton

If a reloid is both complete and co-complete it is discrete

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 f is complete iff there exists a function G : \mho \rightarrow \mathfrak{F} such that
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.

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