Open And Discrete
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Open And Discrete
Let \( \displaystyle f \) be a non-constant holomorphic function defined on a region \( \displaystyle \Omega \) of \( \mathbb{C} \). Show that \( \displaystyle f \) is open and discrete.
Note that "discrete" means that for all \( \displaystyle y \in \mathbb{C} \, , \, f^{-1} \left( \{y \} \right) \) contains only isolated points.
Note that "discrete" means that for all \( \displaystyle y \in \mathbb{C} \, , \, f^{-1} \left( \{y \} \right) \) contains only isolated points.
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