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Strongly meager sets can be quite big

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Abstract

AssumeCH. There exists a strongly meager setX⊆2ω and a continuous functionF: 2ω → 2ω such thatF″ (X)=2ω. The analogous statement for the strong measure zero, the notion dual to strongly meager, is false.

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Author notes

  1. Andrzej Nowik

    Present address: Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81 - 825, Sopot, Poland

Authors and Affiliations

  1. Department of Mathematics, Boise State University, 83725, Boise, ID, USA

    Tomek Bartoszynski

  2. Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80 - 952, Gdańsk, Poland

    Andrzej Nowik

  3. Department of Mathematics, WSRP, Siedlce, Poland

    Tomasz Weiss

Authors
  1. Tomek Bartoszynski
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  2. Andrzej Nowik
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  3. Tomasz Weiss
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Corresponding author

Correspondence to Tomek Bartoszynski.

Additional information

The first author was partially supported by NSF grant DMS 9971282 and the Alexander von Humboldt Foundation.

The second author was partially supported by grant BW 5100-5-0231-2.

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Bartoszynski, T., Nowik, A. & Weiss, T. Strongly meager sets can be quite big. Isr. J. Math. 139, 237–251 (2004). https://doi.org/10.1007/BF02787551

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  • DOI: https://doi.org/10.1007/BF02787551

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