Pointwise convergence and the Wadge hierarchy
Pointwise convergence and the Wadge hierarchy
Let \(X\) be a separable metrizable space. Let \(\mathcal C_p(X)\) (\(\mathcal C_p^*(X)\), respectively) be the space of real-valued continuous functions (bounded real-valued continuous functions, respectively) on \(X\). The space \(\mathcal C_p(X)\) with its Borel structure generated by the topology of pointwise convergence is considered as a subset of a standard Borel space. The main result of the paper reads as follows. If \(X\) is a \(\Sigma _1^1\) separable metrizable space which is not \(\sigma \)-compact, then \(\mathcal C_p(X)\) and \(\mathcal C_p^*(X)\) are Borel-\(\Pi _1^1\)-complete.
- University of Udine Italy
Function spaces in general topology, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Wadge hierarchy, pointwise convergence, Descriptive set theory, function spaces, analytic sets
Function spaces in general topology, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Wadge hierarchy, pointwise convergence, Descriptive set theory, function spaces, analytic sets
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