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Finer topologies on pointsets in Polish spaces

Volume 261 / 2023

Howard Becker Fundamenta Mathematicae 261 (2023), 99-131 MSC: Primary 03E15; Secondary 03E60. DOI: 10.4064/fm211-11-2022 Published online: 30 January 2023

Abstract

Assuming $\mathrm{AD}_{\mathbb R}$, we generalize to higher levels some classical theorems about the first level of the projective hierarchy. The theorems involve the relationships between a pointclass and the type of finer topology that pointsets in that pointclass admit. One such classical theorem is this: A pointset $Y$ in a Polish space is Borel iff there exists a Polish topology on $Y$ finer than the usual topology.

Authors

  • Howard BeckerPMB 128, 4711 Forest Dr., Ste. 3
    Columbia, SC 29206, U.S.A.
    e-mail

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