Conjecture For every funcoid $latex f$ and filter $latex \mathcal{X}\in\mathfrak{F}(\mathrm{Src}\,f)$, $latex \mathcal{Y}\in\mathfrak{F}(\mathrm{Dst}\,f)$:

  1. $latex \mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y}
    \Leftrightarrow \forall F \in \mathrm{up}^{\Gamma (\mathrm{Src}\, f ; \mathrm{Dst}\,
    f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y}$;

  2. $latex \langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigsqcap_{F
    \in \mathrm{up}^{\Gamma (\mathrm{Src}\, f ; \mathrm{Dst}\, f)} f} \langle F \rangle
    \mathcal{X}$.

1 thought on “Funcoid corresponding to reloid through lattice Gamma

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