In French, they call “compact à bord régulier” a compact set $K \subset \mathbb{C}$ such that $K=cl(int(K))$ and $\partial K$ is a finite union of piecewise $C^2$, disjoint and orientable (relatively to $K$) arcs. Is there a name for this in English? I haven’t been able to find it.
Edit: I think the boundary of such a set might be called a staircase countour, but I’m not sure. Anyone can confirm?