Let C be the field of complex numbers and let D(z0,m) denote the open
disk with center z0 and radius m. Let U be an open subset of C,
closure of D(a,R) contained in U and f:U->C. Suppose further that
f is analytic on the closure of D(a,R). Proposition: for no r > R is f
analytic on D(a,r). Can this be true? Thank you for reading.