I'm wondering if a compact set $A\subset\mathbb{C}$ satisfying the properties that


• $A$ and its complement have finitely many connected components


• every connected component of $\partial A$ is the image of a path (say piecewise analytic, or $C^1$)


has a standard name? I'm not sure "set with rectifiable boundary" qualifies, but maybe I'm mistaken. In any case I'm looking for a shorter term if at all possible.


Thank you in advance for any pointer/suggestion.



What are these compact sets called?
I'll finaly settle for "a cutout compact set" for want of a better term. But I think this word expresses well the "finitely many" (connected components, non-smooth points) side of the object, which is what I wanted to highlight.


