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===Riemann-Hurwitz formula===
{{main|Riemann-Hurwitz formula}}
the '''Riemann–Hurwitz formula''', named after [[Bernhard Riemann]] and [[Adolf Hurwitz]], describes the relationship of the [[Euler characteristic]]s of two [[Surface (topology)|surface]]s when one is a ''ramified covering'' of the other. It therefore connects [[Ramification (mathematics)|ramification]] with [[algebraic topology]], in this case. It is a prototype result for many others, and is often applied in the theory of [[Riemann surface]]s (which is its origin) and [[algebraic curve]]s.
==== Statement ====
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