I’ve asked this question at math.StackExchange.com Let $latex \delta$ be a proximity. A set $latex A$ is connected regarding $latex \delta$ iff $latex \forall X,Y \in \mathscr{P} A \setminus \{ \emptyset \} : \left( X \cup Y = A \Rightarrow X \mathrel{\delta}…

read moreJust a few seconds ago I had an idea how to generalize both funcoids and reloids. Consider a precategory, whose objects are sets product $latex \times$ of filters on sets ranging in morphisms of this category operations $latex \mathrm{dom}$ and $latex \mathrm{im}$…

read moreI’ve proved this my conjecture: $latex g \circ f = \bigsqcap \left\{ G \circ F \,|\, F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \right\}$ for every composable funcoids $latex f$ and $latex g$. See my book (in the current draft the…

read moreIn the draft of my book there was an error. I’ve corrected it today. Wrong: $latex \forall a, b \in \mathfrak{A}: ( \mathrm{atoms}\, a \sqsubset \mathrm{atoms}\, b \Rightarrow a \subset b)$. Right: $latex \forall a, b \in \mathfrak{A}: ( a \sqsubset b…

read moreI’ve proved: There exists a filter which cannot be (both weakly and strongly) partitioned into ultrafilters. It is an easy consequence of a lemma proved by Niels Diepeveen (also Karl Kronenfeld has helped me to elaborate the proof). See the preprint of…

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