Abstract:
What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T0 or T1, but not T2 (i.e. not Hausdorff)? This question has been addressed by Selivanov in a series of papers centred on algebraic domains. And recently it has been considered by de Brecht for quasi-Polish spaces, a framework that contains both countably based continuous domains and Polish spaces. In this paper, we present alternative unifying topological spaces, that we call approximation spaces. They are exactly the spaces for which player Nonempty has a stationary strategy in the Choquet game. A natural proper subclass of approximation spaces coincides with the class of quasi-Polish spaces. We study the Borel and Hausdorff difference hierarchies in approximation spaces, revisiting the work done for the other topological spaces. We also consider the problem of effectivization of these results. Copyright © Cambridge University Press 2014.
Registro:
Documento: |
Artículo
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Título: | Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization |
Autor: | Becher, V.; Grigorieff, S. |
Filiación: | FCEyN, Universidad de Buenos Aires, CONICET, Buenos Aires, Argentina LIAFA, CNRS, Université Paris Diderot - Paris 7, France Laboratoire International Associé INFINIS, Universidad de Buenos Aires, Université Paris Diderot-Paris 7, France
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Palabras clave: | Set theory; Algebraic domains; Approximation spaces; Continuous domain; Descriptive set theory; Difference hierarchies; Hausdorff; Hausdorff hierarchy; Topological spaces; Topology |
Año: | 2015
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Volumen: | 25
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Número: | 7
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Página de inicio: | 1490
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Página de fin: | 1519
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DOI: |
http://dx.doi.org/10.1017/S096012951300025X |
Título revista: | Mathematical Structures in Computer Science
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Título revista abreviado: | Math. Struct. Comput. Sci.
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ISSN: | 09601295
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09601295_v25_n7_p1490_Becher |
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Citas:
---------- APA ----------
Becher, V. & Grigorieff, S.
(2015)
. Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization. Mathematical Structures in Computer Science, 25(7), 1490-1519.
http://dx.doi.org/10.1017/S096012951300025X---------- CHICAGO ----------
Becher, V., Grigorieff, S.
"Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization"
. Mathematical Structures in Computer Science 25, no. 7
(2015) : 1490-1519.
http://dx.doi.org/10.1017/S096012951300025X---------- MLA ----------
Becher, V., Grigorieff, S.
"Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization"
. Mathematical Structures in Computer Science, vol. 25, no. 7, 2015, pp. 1490-1519.
http://dx.doi.org/10.1017/S096012951300025X---------- VANCOUVER ----------
Becher, V., Grigorieff, S. Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization. Math. Struct. Comput. Sci. 2015;25(7):1490-1519.
http://dx.doi.org/10.1017/S096012951300025X