funcoid corresponding to reloid


Funcoid corresponding to reloid through lattice Gamma ★★

Author(s): Porton

\begin{conjecture} For every reloid $f$ and $\mathcal{X} \in \mathfrak{F} (\operatorname{Src} f)$, $\mathcal{Y} \in \mathfrak{F} (\operatorname{Dst} f)$: \begin{enumerate} \item $\mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y} \Leftrightarrow \forall F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y}$; \item $\langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigcap_{F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f} \langle F \rangle \mathcal{X}$. \end{enumerate} \end{conjecture}

It's proved by me in \href [this online article]{http://www.mathematics21.org/binaries/funcoids-are-filters.pdf}.

Keywords: funcoid corresponding to reloid

Restricting a reloid to lattice Gamma before converting it into a funcoid ★★

Author(s): Porton

\begin{conjecture} $(\mathsf{FCD}) f = \bigcap^{\mathsf{FCD}} (\Gamma (A ; B) \cap \operatorname{GR} f)$ for every reloid $f \in \mathsf{RLD} (A ; B)$. \end{conjecture}

Keywords: funcoid corresponding to reloid; funcoids; reloids

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