∀ {α' : Type u_3} {β : Type u_4} [inst : TopologicalSpace α'] [inst_1 : Zero β] [T2Space α']
  [inst_3 : TopologicalSpace β] {U : Set α'},
  IsOpen U → ∀ {f : ↑U → β}, Continuous f → HasCompactSupport f → Continuous (Function.extend Subtype.val f 0)