Originally Posted by

**ENRIQUESTEFANINI** I'm very sorry I didn't explain myself clearly. No. I'm only told f is analytic

on the closure of the disk. However, first I should have wondered if there

is such D(a,r) in S (I forgot to establish that D(a,r) must be contained in

S, but reading your proof I see you understood it that way). This is a

purely topological question and your proof answers it in the affirmative.

So the question remains. Is there a D(a,r) in S such that r > R and f

analytic on D(a,r)? Best regards and thank you for your time.

Enrique