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Compact funcoids

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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.

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