Abstract The paper is of pedagogical nature and is aimed mainly at students.
It presents a detailed proof of the well-known fact that if the
boundary of an open set in ${R}^n$ is of class $C^k$, $k\geq
2$, so is the signed distance to the boundary function. This
function plays an important role in problems of Analysis and
Geometry. The presented proof could give a teacher a good
opportunity to discuss important theorems in Calculus.
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