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Any subset of Baire space is a union of a boldface $\Delta_2^0$ set and a set with no isolated points. Anybody know how to prove this?
I'm trying to do due diligence and determine whether this is known, trivial, original, etc. I have a proof of:
Theorem: If $S\subseteq \mathbb{N}^{\mathbb{N}}$ then $S=X\cup Y$ for some $X$ which is ...
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