Is it possible to show that for a neither open nor closed subset $ A \subset \mathbb{R}^n$, $\partial A \cap A$ is a closed set in $\mathbb{R}^n$?
2026-04-03 12:51:03.1775220663
Intersection between a set and its boundary is a closed set?
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No. $A=\mathbb{Q}$ has $\mathbb{R}$ as its boundary so $A \cap \partial A = A$ is neither open nor closed.