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I am referring to this answer : https://math.stackexchange.com/a/273269/1162293

I do not see why the argument let us tell that ramification points are a closed subset of $X$. Has someone some more details to give ?

Florian Manzini
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – CrSb0001 May 19 '23 at 15:21

1 Answers1

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If $f: X \to Y$ is not ramified at $x \in X$, then it is a local homeomorphism around $x$. I.e., there is an open neighborhood $x \in U \subseteq X$ s.t. $f|_U$ is a local homeomorphism. Hence $f$ is unramified at all points of $U$.

That shows that the complement of the ramified points is open.

Johann Birnick
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