Let $ A \subset X$ of a metric space. Define $bd(A) = \overline{\rm A} \cap (\overline{\rm A^c)} $ to be the boundary of $A.$
Show that If $ x \in bd(\overline{\rm A^c}),$ then $x \in bd(A)$
(I have tried proof by contradiction but am stuck)
2026-04-08 20:49:06.1775681346
Show if x lies in this specified boundary, it must lie in this specific one as well
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$bd(\overline{A^c})=\overline{\overline{A^c}}\cap \overline{\overline{A^c}^c}$
$\overline{\overline{A^c}}=A^c$, $\overline{A^c}^c\subset A$
implies that $bd(A)\subset A^c\cap \overline{A}$