inner reloid


Inner reloid through the lattice Gamma ★★

Author(s): Porton

\begin{conjecture} $(\mathsf{RLD})_{\operatorname{in}} f = \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f$ for every funcoid $f$. \end{conjecture}

Counter-example: $(\mathsf{RLD})_{\operatorname{in}} f \sqsubset \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f$ for the funcoid $f = (=)|_\mathbb{R}$ is proved in \href[this online article]{http://www.mathematics21.org/binaries/funcoids-are-filters.pdf}.

Keywords: filters; funcoids; inner reloid; reloids

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