Pointwise convergence and the Wadge hierarchy
Andretta, Alessandro ; Marcone, Alberto
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 159-172 / Harvested from Czech Digital Mathematics Library
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We show that if $X$ is a $\Sigma _1^1$ separable metrizable space which is not $\sigma $-compact then $C_p^* (X)$, the space of bounded real-valued continuous functions on $X$ with the topology of pointwise convergence, is Borel-$\Pi _1^1$-complete. Assuming projective determinacy we show that if $X$ is projective not $\sigma $-compact and $n$ is least such that $X$ is $\Sigma _n^1$ then $C_p (X)$, the space of real-valued continuous functions on $X$ with the topology of pointwise convergence, is Borel-$\Pi _n^1$-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.

Publié le : 2001-01-01
Classification:  03E15,  28A05,  54C35,  54H05 
@article{119231,
     author = {Alessandro Andretta and Alberto Marcone},
     title = {Pointwise convergence and the Wadge hierarchy},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {159-172},
     zbl = {1052.03023},
     mrnumber = {1825380},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119231}
}

Andretta, Alessandro; Marcone, Alberto. Pointwise convergence and the Wadge hierarchy. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 159-172. http://gdmltest.u-ga.fr/item/119231/

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