## Classical Descriptive Set Theory |

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algebra analytic sets assume Baire space Banach space bijection Borel function Borel measure Borel sets called Cantor set class of sets clearly clopen closed set closed subspace comeager compact metrizable compact sets Consider contains continuous function continuous preimages converges define denote equivalence relation Exercise F C X finite given Gs set homeomorphic II}-complete II}-rank infinite Kechris Lemma length(s Lusin meager measurable space metrizable space Moschovakis nonempty open sets notation open nbhd open sets ordinal pairwise disjoint player plays pointwise Polish group Polish space Projective Determinacy Proof prove pruned tree r-algebra rank recursion second countable separable Banach space sequence set A C X set theory sets in Polish Show standard Borel space Theorem topological space uniformization unique Wadge well-founded well-founded relation winning strategy wins iff zero-dimensional