descriptive set theory – Universal Set for $\mathcal{A}\Pi^1_1$ Answer

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descriptive set theory – Universal Set for $\mathcal{A}\Pi^1_1$

I’m probably missing something easy but I’m having trouble with the first part of Kechris’s Classical Descriptive Set Theory, Exercise 29.17, the first part:

For an uncountable Polish space $Y$show that there is a $Y$-universal set for $\mathcal{A}\Pi^1_1$where $\mathcal{A}$ is the Souslin operator.

I know wlog we can take $Y = \mathbb{N}^\mathbb{N}$ and then we have easy examples of $\mathbb{N}^\mathbb{N}$-universal sets for $\Pi^1_1$but I can’t seem to make the leap to $\mathcal{A}\Pi^1_1$.

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