intrinsicFrontier_union_intrinsicInterior

English

The frontier and interior union equals the closure.

Русский

Граница и interior образуют замыкание.

LaTeX

$$$\\operatorname{intrinsicFrontier}_{\\mathbb{k}}(s) \\cup \\operatorname{intrinsicInterior}_{\\mathbb{k}}(s) = \\operatorname{intrinsicClosure}_{\\mathbb{k}}(s)$$$

Lean4

@[simp]
theorem intrinsicFrontier_union_intrinsicInterior (s : Set P) :
    intrinsicFrontier 𝕜 s ∪ intrinsicInterior 𝕜 s = intrinsicClosure 𝕜 s := by
  rw [union_comm, intrinsicInterior_union_intrinsicFrontier]

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