Hi this was a question in my exam and i can't solve it i search and i founed equivalence relation between the equality of the union and the boundary of these sets and i still can't solve it. my teacher said to me it less than 5 line any help? Let$ A,B \subset X$ where $\bar A \cap B = \bar B \cap A = \emptyset $ Proof that $ \operatorname{int}(A \cup B)=\operatorname{int}(A)\cup \operatorname{int}(B).$
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By hypothesis, no point in A is in the closure of B and no point in B is in the closure of A, so the interior of A and that of B are disjoint sets. This implies the required equality.
