### A vaguely formulated problem

Consider funcoid $latex \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ (restricted identity funcoids on Frechet filter on some infinite set). Naturally $latex 1\in\mathrm{up}\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ (where $latex 1$ is the identity morphism). But it also holds $latex \top^{\mathsf{FCD}}\setminus 1\in\mathrm{up}\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ (where $latex 1$ is the identity morphism). This result…

### The set of ideals on an infinite join-semilattice is a boolean algebra

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…