# What are these compact sets called?

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.

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How about just a "piecewise smooth set"? –  Lee Mosher May 16 at 11:58