Affiliation:
1. Institute of Discrete Mathematics and Geometry, TU Wien Vienna Austria
2. Dipartimento di Matematica “G. Peano” Università degli Studi di Torino Turin Italy
3. School of Mathematics University of Bristol Bristol UK
Abstract
AbstractIn the context of generalized descriptive set theory, we systematically compare and analyze various notions of Polish‐like spaces and standard ‐Borel spaces for an uncountable (regular) cardinal satisfying . As a result, we obtain a solid framework where one can develop the theory in full generality. We also provide natural characterizations of the generalized Cantor and Baire spaces. Some of the results obtained considerably extend previous work from Coskey and Schlicht (Fund. Math. 232 (2016) 227–248), Galeotti (Ph.D. thesis, Universität Hamburg, 2019), and Lücke and Schlicht (Israel J. Math. 209 (2015) 421–461), and answer some questions contained therein.
Funder
Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
Engineering and Physical Sciences Research Council
Austrian Science Fund
Horizon 2020 Framework Programme
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