The below is wrong, because pointfree funcoids between boolean algebras are not the same as 2-staroids between boolean algebras. It was an error. I have just discovered that the set of ideals on an infinite join-semilattice is a boolean algebra (moreover it…

read moreI conjectured certain formula for the complete lattice generated by a strong partitioning of an element of complete lattice. Now I have found a beautiful proof of a weaker statement than this conjecture. (Well, my proof works only in the case of…

read moreIn this post I defined strong partitioning of an element of a complete lattice. For me it was seeming obvious that the complete lattice generated by the set $latex S$ where $latex S$ is a strong partitioning is equal to $latex \left\{…

read moreLet $latex \mathfrak{A}$ is a complete lattice. Let $latex a\in\mathfrak{A}$. I will call weak partitioning of $latex a$ a set $latex S\in\mathscr{P}\mathfrak{A}\setminus\{0\}$ such that $latex \bigcup{}^{\mathfrak{A}}S = a \text{ and } \forall x\in S: x\cap^{\mathfrak{A}}\bigcup{}^{\mathfrak{A}}(S\setminus\{x\}) = 0$. I will call strong partitioning…

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