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Strong measure zero in separable metric spaces and Polish groups

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Abstract

The notion of strong measure zero is studied in the context of Polish groups and general separable metric spaces. An extension of a theorem of Galvin, Mycielski and Solovay is given, whereas the theorem is shown to fail for the Baer–Specker group \({{\mathbb{Z}^{\omega}}}\). The uniformity number of the ideal of strong measure zero subsets of a separable metric space is examined, providing solutions to several problems of Miller and Steprāns (Ann Pure Appl Logic 140(1–3):52–59, 2006).

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Área de la Investigación Científica, Circuito exterior, Ciudad Universitaria, 04510, Mexico, D.F., Mexico

    Michael Hrušák

  2. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/104, 1040, Vienna, Austria

    Wolfgang Wohofsky

  3. Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 160 00, Prague 6, Czech Republic

    Ondřej Zindulka

Authors
  1. Michael Hrušák
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  2. Wolfgang Wohofsky
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  3. Ondřej Zindulka
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Corresponding author

Correspondence to Michael Hrušák.

Additional information

Work on this project was partially conducted during the third author’s stay at the Centro de Ciencias Matemáticas, Universidad Nacional Autonóma de México supported by CONACyT Grant No. 125108. The first author gratefully acknowledges support from PAPIIT Grant IN 108014 and CONACyT Grant 177758. The work of the second author was partially supported by the Czech Ministry of Education Grant 7AMB13AT011: Combinatorics and Forcing.

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Hrušák, M., Wohofsky, W. & Zindulka, O. Strong measure zero in separable metric spaces and Polish groups. Arch. Math. Logic 55, 105–131 (2016). https://doi.org/10.1007/s00153-015-0459-2

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