class PiBase.SubparacompactSpace (X : Type u) [TopologicalSpace X] : Prop

• locallyFinite_refinement (α : Type u) (s : α → Set X) : (∀ (a : α), IsOpen (s a)) → ⋃ (a : α), s a = Set.univ → ∃ (β : Type u) (t : β → Set X), (∀ (b : β), IsClosed (t b)) ∧ ⋃ (b : β), t b = Set.univ ∧ Sigma (fun {α : Type u} => LocallyFinite) t ∧ ∀ (b : β), ∃ (a : α), t b ⊆ s a