= Eliashberg–Gromov rigidity theorem
{c}
{title2=$\operatorname{Symp}(M,\omega)\text{ is }C^0\text{-closed in }\operatorname{Diff}(M)$}
A locally uniform limit of <symplectomorphisms> that is a smooth diffeomorphism is symplectic. By <capacity preservation under uniform limits> and <linear capacity rigidity>, its derivative is symplectic or <anti-symplectic>. Repeat this argument after taking the product of every map with the identity on a symplectic plane. An anti-symplectic derivative on the original factor and a symplectic derivative on the added factor would give neither sign on the product, a contradiction. The argument uses <symplectic capacities> in the original and stabilized dimensions.
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