| Title:
|
Pointwise convergence and the Wadge hierarchy (English) |
| Author:
|
Andretta, Alessandro |
| Author:
|
Marcone, Alberto |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
159-172 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Wadge hierarchy |
| Keyword:
|
function spaces |
| Keyword:
|
pointwise convergence |
| MSC:
|
03E15 |
| MSC:
|
28A05 |
| MSC:
|
54C35 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 1052.03023 |
| idMR:
|
MR1825380 |
| . |
| Date available:
|
2009-01-08T19:08:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119231 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
