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Alexandre Eremenko
Alexandre Eremenko
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Let $M$ be a $1$-dimenaionaldimensional complex manifold. Let $A$ be the space of all holomorphic functions $f:M\to \mathbb{C}$ such that either $f$ is a constant function or every level set $f^{-1}(c)$ is a finite (probeblyprobably empty) set. Is $A$ an algebra of functions? Is its closurclosure, with respect to topology of uniform convergence on compact subsets, equaulequal to space of all holomorphic functions from $M$ to $\mathbb{C}$?

Let $M$ be a $1$-dimenaional complex manifold. Let $A$ be the space of all holomorphic functions $f:M\to \mathbb{C}$ such that either $f$ is a constant function or every level set $f^{-1}(c)$ is a finite (probebly empty) set. Is $A$ an algebra of functions? Is its closur, with respect to topology of uniform convergence on compact subsets, equaul to space of all holomorphic functions from $M$ to $\mathbb{C}$?

Let $M$ be a $1$-dimensional complex manifold. Let $A$ be the space of all holomorphic functions $f:M\to \mathbb{C}$ such that either $f$ is a constant function or every level set $f^{-1}(c)$ is a finite (probably empty) set. Is $A$ an algebra of functions? Is its closure, with respect to topology of uniform convergence on compact subsets, equal to space of all holomorphic functions from $M$ to $\mathbb{C}$?

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Ali Taghavi
Ali Taghavi
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A generalization of polynomial algebra toon a Riemann surface

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Ali Taghavi
Ali Taghavi
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A generalization of polynomial algebra to a Riemann surface

Let $M$ be a $1$-dimenaional complex manifold. Let $A$ be the space of all holomorphic functions $f:M\to \mathbb{C}$ such that either $f$ is a constant function or every level set $f^{-1}(c)$ is a finite (probebly empty) set. Is $A$ an algebra of functions? Is its closur, with respect to topology of uniform convergence on compact subsets, equaul to space of all holomorphic functions from $M$ to $\mathbb{C}$?