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Beyond Erdős-Kunen-Mauldin: Shift-compactness properties and Singular sets

Miller, Harry I., Miller-Van Wieren, Leila and Ostaszewski, Adam (2020) Beyond Erdős-Kunen-Mauldin: Shift-compactness properties and Singular sets. Topology and its Applications. ISSN 0166-8641 (In Press)

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Abstract

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 e§ective 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
Divisions: Mathematics
Date Deposited: 05 Nov 2020 15:06
Last Modified: 05 Nov 2020 15:07
URI: http://eprints.lse.ac.uk/id/eprint/107143

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