Pointwise convergence and the Wadge hierarchy
نویسندگان
چکیده
We show that if X is a Σ 1 separable metrizable space which is not σ-compact then C p (X), the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel-Π 1 -complete. Assuming projective determinacy we show that if X is projective not σ-compact and n is least such that X is Σ1n then Cp(X), the space of real-valued continuous functions on X with the topology of pointwise convergence, is Borel-Π1n-complete. We also prove a simultaneous improvement of theorems of Christensen and Kechris regarding the complexity of a subset of the hyperspace of the closed sets of a Polish space.
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