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Math Help - constant analytic function regular in a region G

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by vnca1 View Post
    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?
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  3. #3
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    Thank you very much. Your answer is probably the shortest yet a very useful one.
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