Thread: constant analytic function regular in a region G

Hi everybody, could you explain to me, as simple as possible, why an analytic function
regular in a domain G (open and connected) cannot be constant throughout a sub-domain
of G without being a constant throughout all of G?

Thank you very much.

Originally Posted by vnca1

Hi everybody, could you explain to me, as simple as possible, why an analytic function
regular in a domain G (open and connected) cannot be constant throughout a sub-domain
of G without being a constant throughout all of G?

Thank you very much.

By the identity theorem.
Do you see why?

Thank you very much. Your answer is probably the shortest yet a very useful one.