**Conjecture**If , are complete funcoids (generalized closures) then is a complete funcoid (generalized closure).

See Algebraic General Topology for definitions of used concepts.

Below is also a weaker conjecture:

**Conjecture**If , are binary relations then is a binary relation; or equivalently, for any binary relations and .

The author has found a counterexample against this weaker conjecture and thus against the main conjecture. The example is and . It is simple to show that where is the Fréchet filter and thus .

See the section "Some counter-examples" in the online article "Funcoids and Reloids" for details.

## Bibliography

*Victor Porton. Algebraic General Topology

* indicates original appearance(s) of problem.