Classification of the spaces C_p*(X) within the Borel-Wadge hierarchy for a projective space X

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10285023" target="_blank" >RIV/00216208:11320/15:10285023 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/15:00442124
Result on the web
<a href="http://dx.doi.org/10.1016/j.topol.2014.12.021" target="_blank" >http://dx.doi.org/10.1016/j.topol.2014.12.021</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2014.12.021" target="_blank" >10.1016/j.topol.2014.12.021</a>

Result language
angličtina
Original language name
Classification of the spaces C_p*(X) within the Borel-Wadge hierarchy for a projective space X
Original language description
We study the complexity of the space $C^*_p(X)$ of bounded continuous functions with the topology of pointwise convergence. We are allowed to use descriptive set theoretical methods, since for a separable metrizable space $X$, the measurable space of Borel sets in $C^*_p(X)$ (and also in the space $C_p(X)$ of all continuous functions) is known to be isomorphic to a subspace of a standard Borel space. It was proved by A. Andretta and A. Marcone % in [Pointwise convergence and the Wadge hierarchy. Comment. Math. Univ. Carolin., 42(1):159âEUR"172, 2001] that if $X$ is a $sigma$-compact metrizable space, then the measurable spaces $C_p(X)$ and $C^*_p(X)$ are standard Borel and if $X$ is a metrizable analytic space which is not $sigma$-compact then the spaces of continuous functions are Borel-$Pi^1_1$-complete. They also determined under the assumption of projective determinacy (textsf{PD}) the complexity of $C_p(X)$ for any projective space $X$ and asked whether a similar result holds
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GP14-06989P" target="_blank" >GP14-06989P: Quasiorder of curves with respect to open, monotone and confluent mappings</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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