# Intersection of complete funcoids (Solved)

 Importance: Medium ✭✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: complete funcoid funcoid generalized closure
 Posted by: porton on: August 9th, 2007
 Solved by: Porton, Victor
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.

1) definitions of the used concepts (to make the statement self-contained)

2) motivation (why this is important, examples, ...)

At the present state, this text is unfortunately not very useful for someone not acquainted with your manuscripts.