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

What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T<inf>0</inf> or T<inf>1</inf>, but not T<inf>2</inf> (i.e. not Hausdorff)? This question has been addressed by Selivanov in a series...

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Autor principal:	Becher, Verónica Andrea
Publicado:	2015
Materias:	Set theory Algebraic domains Approximation spaces Continuous domain Descriptive set theory Difference hierarchies Hausdorff Hausdorff hierarchy Topological spaces Topology
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09601295_v25_n7_p1490_Becher http://hdl.handle.net/20.500.12110/paper_09601295_v25_n7_p1490_Becher
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_09601295_v25_n7_p1490_Becher
record_format	dspace
spelling	paper:paper_09601295_v25_n7_p1490_Becher2023-06-08T15:57:33Z Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization Becher, Verónica Andrea Set theory Algebraic domains Approximation spaces Continuous domain Descriptive set theory Difference hierarchies Hausdorff Hausdorff hierarchy Topological spaces Topology What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T<inf>0</inf> or T<inf>1</inf>, but not T<inf>2</inf> (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. Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09601295_v25_n7_p1490_Becher http://hdl.handle.net/20.500.12110/paper_09601295_v25_n7_p1490_Becher
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Set theory Algebraic domains Approximation spaces Continuous domain Descriptive set theory Difference hierarchies Hausdorff Hausdorff hierarchy Topological spaces Topology
spellingShingle	Set theory Algebraic domains Approximation spaces Continuous domain Descriptive set theory Difference hierarchies Hausdorff Hausdorff hierarchy Topological spaces Topology Becher, Verónica Andrea Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
topic_facet	Set theory Algebraic domains Approximation spaces Continuous domain Descriptive set theory Difference hierarchies Hausdorff Hausdorff hierarchy Topological spaces Topology
description	What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T<inf>0</inf> or T<inf>1</inf>, but not T<inf>2</inf> (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.
author	Becher, Verónica Andrea
author_facet	Becher, Verónica Andrea
author_sort	Becher, Verónica Andrea
title	Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
title_short	Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
title_full	Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
title_fullStr	Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
title_full_unstemmed	Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
title_sort	borel and hausdorff hierarchies in topological spaces of choquet games and their effectivization
publishDate	2015
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09601295_v25_n7_p1490_Becher http://hdl.handle.net/20.500.12110/paper_09601295_v25_n7_p1490_Becher
work_keys_str_mv	AT becherveronicaandrea borelandhausdorffhierarchiesintopologicalspacesofchoquetgamesandtheireffectivization
_version_	1768543093834907648

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

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