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Let $X,Y$ be two compact Riemann surfaces. Let $a \in X$ and $f : X-\{a\} \to Y$ be a injective holomorphic map. Prove that $a$ is removable singularity of $f$.

I want to apply Riemann removable singularity theorem somehow but I am unable to get it. Any help will be appreciated.

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After trying I got similar question over here

Extending isomorphism of punctured Riemann surfaces

But still answer over there is not clear to me.

Sorry for the duplicate!

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