2021/07/06 by Claudio Agostini, Agostini, Claudio, Luca Motto Ros +3
Computer Science · Mathematics · #03E15 #54E99 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · doi:10.48550/arxiv.2107.02587
openalex publication_date 2021/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of generalized descriptive set theory, we systematically compare and analyze various notions of Polish-like spaces and standard κ-Borel spaces for κ an uncountable (regular) cardinal satisfying κ<κ = κ. 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-Schlicht 2016, Galeotti 2019, Luecke-Schlicht 2015], and answer some questions contained therein.