This question is from Ponnusamy and silvermann Complex variables with applications , chapter- Analytic Continuation.
Note: If a function f is analytic in domain D then author represent them as (f,D).
Is it possible that function elements $(f, D_1) $ and $(g ,D_2) $ can be connected by an infinite chain of functional elements , but by no finite subchain.
I am not sure but intution says that it will not be possible.
Can you please help me prove it or find an counterexample.I am sorry , I can't provide anything as attempt in this question.
This is based on a lot of ignorance but, suppose the nth domain has size 1/2^n. Can the limit of these domains reach a domain which is 1 away?