Suppose that $f:X \to Y$ is a branched cover of Riemann surfaces and a covering map of degree one outside of the ramification points. Then is $f$ a homeomorphism?
2025-01-13 05:57:18.1736747838
Degree one branched cover is a homeomorphism
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Yes $f$ is an homeomorphism since the the cardinal of the fibre of a branched point is inferior to the degree. I assume of course that the surfaces are closed.