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Beyond Erdős-Kunen-Mauldin: shift-compactness properties and singular sets

Miller, Harry I., Miller-Van Wieren, Leila and Ostaszewski, Adam (2021) Beyond Erdős-Kunen-Mauldin: shift-compactness properties and singular sets. Topology and its Applications, 291. ISSN 0166-8641

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Identification Number: 10.1016/j.topol.2021.107605


The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of R which is Baire (= has the Baire property, BP) or measurable is shift-compact: it contains some subsequence of any null sequence to within translation by an element of the set. Here effective proofs are recognized to yield (i) analogous category and Haar-measure metrizable generalizations for Baire groups and locally compact groups respectively, and (ii) permit under V = L construction of co-analytic shift-compact subsets of R with singular properties, e.g. being concentrated on Q, the rationals.

Item Type: Article
Official URL:
Additional Information: © 2021 Elsevier B.V.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 05 Nov 2020 15:21
Last Modified: 09 Jan 2022 00:00

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