Mumford's compactness theorem
= Mumford's compactness theorem
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{title2=$\mathcal M_g^\varepsilon\text{ is compact}$}
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The subset of the unmarked <moduli space of Riemann surfaces> with <hyperbolic systole> at least $\varepsilon>0$ is <compact> for fixed <genus> $g\geq2$. Use a <Bers pants decomposition theorem> bound, finitely many topological decomposition types and <Dehn twists> to place representatives in finitely many <compact> boxes in <Fenchel–Nielsen coordinates>.