have : (Set.univ : Set X) = ⋂ i : Empty, i.rec := by
  rw [Set.iInter_of_empty]
X : Type
T : Topology X
⊢ T.isOpen Set.univ
X : Type
T : Topology X
this : Set.univ = ⋂ i, Empty.rec (fun x => Set X) i
⊢ T.isOpen Set.univ