If we should speak of a function f that is analytic in a set $S$ which is not open, it is to be understood that if is analytic in an open set $U$ containing $S$
Is it correct to illustrate this in a broken (dotted/dashed) circle with center $z_0$ (for example) that is inside another bigger circle with boundary not dashed/broken?
(I can't post my illustration because you know) Thanks