I’ve proved the following (for every funcoids $latex f$ and $latex g$): Statement $latex \mathrm{up}\, (f \sqcap^{\mathsf{FCD}} g) \subseteq \bigcup \{ \mathrm{up}\, (F \sqcap^{\mathsf{FCD}} G) \mid F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \}$ or equivalently: If $latex Z\in\mathrm{up}\, (f \sqcap^{\mathsf{FCD}}…

read morehttps://endofgospel.wordpress.com/2017/01/09/mathematicians-from-god/

read moreI’ve proved the following lemma: Lemma Let for every $latex X, Y \in S$ and $latex Z \in \mathrm{up} (X \sqcap^{\mathsf{FCD}} Y)$ there is a $latex T \in S$ such that $latex T \sqsubseteq Z$. Then for every $latex X_0, \ldots, X_n…

read moreAfter prayer in tongues and going down anointment of Holy Spirit I proved this conjecture about funcoids. The proof is currently located in this PDF file. Well, the proof is for special cases of distributive lattices, but more general case seems not…

read moreNew conjecture: Conjecture $latex \mathrm{up} (f \sqcap^{\mathsf{FCD}} g) \subseteq \{ F \sqcap G \mid F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \}$ for all funcoids $latex f$, $latex g$ (with corresponding sources and destinations). Looks trivial? But how to (dis)prove it?

read moreIn this draft I present some definitions and conjectures on how to generalize filter bases for more general filtrators (such as the filtrator of funcoids). This is a work-in-progress. This seems an interesting research by itself, but I started to develop it…

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