Consider funcoid $\mathrm{id}^{\mathsf{FCD}}_{\Omega}$ (restricted identity funcoids on Frechet filter on some infinite set).
Naturally $1\in\mathrm{up}\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ (where $1$ is the identity morphism).
But it also holds $\top^{\mathsf{FCD}}\setminus 1\in\mathrm{up}\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ (where $1$ 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 $\mathrm{up}$ (let’s denote it $\mathrm{up}'$) such that $1\in\mathrm{up}'\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ but $\top^{\mathsf{FCD}}\setminus 1\notin\mathrm{up}'\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$.
Currently I cannot formulate this problem exactly (what is $\mathrm{up}'$?) but I think (if you read my book) you can understand what I want.