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We define a Polish topology inspired from the Gandy-Harrington topology andshow how it can be used to prove Silver's dichotomy theorem while remaining inthe Polish realm. In this topology, a $\Pi^1_1$ equivalence relation decomposesinto a "sum" of a clopen relation and a meager one. We characterize it as thelargest regular toplogy with a basis included in $\Sigma^1_1$.

A note on an effective Polish topology and Silver's Dichotomy theorem