Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization

• Autores: Becher, Veronica Andrea; Grigoreff, Serge
• Año de publicación: 2015
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Borel Hierarchy; Choquet Games; Approximation Spaces; Quasi Metric Spaces
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Grigoreff, Serge. Université Paris Diderot - Paris 7; Francia. Centre National de la Recherche Scientifique; Francia