Conjecture For every composable funcoids $f$ and $g$ we have $g \circ f = \bigcap \{ \uparrow^{\mathsf{FCD} ( \mathrm{Src}\,f ; \mathrm{Dst}\,g) } ( G \circ F ) \hspace{0.5em} | \hspace{0.5em} F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \}$.

1. porton / Oct 31 2011 20:05

This seems the most important open problem in Algebraic General Topology.

It seems for me that research of multidimensional funcoids and then of compactness of funcoids cannot advance without first solving this problem.