The following problem arose from my attempt to re-express directed topological spaces in terms of funcoids.
Conjecture Let $latex R$ be the complete funcoid corresponding to the usual topology on extended real line $latex [-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\infty\}$. Let $latex \geq$ be the order on this set. Then $latex R\sqcap^{\mathsf{FCD}}\mathord{\geq}$ is a complete funcoid.
Can you be more specific about the content of your article? After reading it, I still have some doubts. Hope you can help me.