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 is not hard to prove but quite counter-intuitive (that is is a paradox).

I think that we should find modified $latex \mathrm{up}$ (let’s denote it $latex \mathrm{up}’$) such that $latex 1\in\mathrm{up}’\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ but $latex \top^{\mathsf{FCD}}\setminus 1\notin\mathrm{up}’\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$.

Currently I cannot formulate this problem exactly (what is $latex \mathrm{up}’$?) but I think (if you read my book) you can understand what I want.