∀ {𝕜 : Type u_4} [inst : LinearOrder 𝕜] [inst_1 : TopologicalSpace 𝕜] [OrderTopology 𝕜] {s : Set 𝕜} {a : 𝕜},
  (∀ x ∈ closure s, Set.Ioo x a ⊆ s) → ∀ᶠ (x : 𝕜) in nhdsWithin a (s ∩ Set.Iio a), s \ {a} ∈ nhds x