# A funcoid related to directed topological spaces

**Conjecture**Let be the complete funcoid corresponding to the usual topology on extended real line . Let be the order on this set. Then is a complete funcoid.

**Proposition**It is easy to prove that is the infinitely small right neighborhood filter of point .

If proved true, the conjecture then can be generalized to a wider class of posets.

See Algebraic General Topology for definitions of used concepts.

## Bibliography

* indicates original appearance(s) of problem.