For this conjecture there was found a counter-example, see this online article. The counter-example states that $latex (\mathsf{RLD})_{\Gamma} f \sqsupset (\mathsf{RLD})_{\mathrm{in}} f \sqsupset (\mathsf{RLD})_{\mathrm{out}} f$ for funcoid $latex f=(=)|_{\mathbb{R}}$. This way I discovered a new function $latex (\mathsf{RLD})_{\Gamma}$ defined by the formula…

read more

I’ve proved yet one conjecture. The proof is presented in this online article. Theorem For every funcoid $latex f$ and filters $latex \mathcal{X}\in\mathfrak{F}(\mathrm{Src}\,f)$, $latex \mathcal{Y}\in\mathfrak{F}(\mathrm{Dst}\,f)$: $latex \mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y} \Leftrightarrow \forall F \in \mathrm{up}^{\Gamma (\mathrm{Src}\, f ; \mathrm{Dst}\, f)} f :…

read more