Let $A,B \subset \mathbb{R}^n$ open and bounded sets with smooth boundary. Does the open and bounded set $A \times B$ have (piecewise) smooth boundary? If so can one write the outer unit normal of $A \times B$ as $(n_A,n_B)$?
2026-04-26 00:09:21.1777162161
Cartesian product of two sets with smooth boundary
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