Prerequisites: Algebraic General Topology.

We may call a compact funcoid a funcoid $ f $ confoirming to the following formula: $ \forall \mathcal{F} \in \mathfrak{F}: ( \left\langle f^{- 1} \right\rangle\mathcal{F} \neq \emptyset \Rightarrow \operatorname{Cor}\left\langle f^{- 1} \right\rangle \mathcal{F} \neq \emptyset) $

This formula is equivalent to $ \forall a \in\operatorname{atoms}\,\operatorname{im}f :\operatorname{Cor} \left\langle f^{- 1} \right\rangle a \neq\emptyset $.

Or should we require that both $ f $ and $ f^{-1} $ conform to this formula?

Then we should prove that a compact funcoid is induced by only one reloid.