A funcoid related to directed topological spaces

The following problem arose from my attempt to re-express directed topological spaces in terms of funcoids.

Conjecture Let R be the complete funcoid corresponding to the usual topology on extended real line [-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\infty\}. Let \geq be the order on this set. Then R\sqcap^{\mathsf{FCD}}\mathord{\geq} is a complete funcoid.

Leave a Reply