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Transfinite sequences of topologies, descriptive complexity, and approximating equivalence relations

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Abstract

We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given equivalence relation. We investigate those.

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Acknowledgments

I thank Assaf Shani for pointing out paper [4] to me. I also thank the referee for a careful reading of the paper and for pointing out a gap, which has been repaired, in one of the arguments in an earlier version of it.

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Authors and Affiliations

  1. Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY, 14853, USA

    Sławomir Solecki

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  1. Sławomir Solecki
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Correspondence to Sławomir Solecki.

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Research supported by NSF grant DMS-1800680.

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Solecki, S. Transfinite sequences of topologies, descriptive complexity, and approximating equivalence relations. Isr. J. Math. 242, 933–953 (2021). https://doi.org/10.1007/s11856-021-2153-x

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  • DOI: https://doi.org/10.1007/s11856-021-2153-x

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