Additivity of the Gerlits–Nagy property and concentrated sets
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- by Boaz Tsaban and Lyubomyr Zdomskyy PDF
- Proc. Amer. Math. Soc. 142 (2014), 2881-2890 Request permission
Abstract:
We settle all problems concerning the additivity of the Gerlits–Nagy property and related additivity numbers posed by Scheepers in his tribute paper to Gerlits. We apply these results to compute the minimal number of concentrated sets of reals (in the sense of Besicovitch) whose union, when multiplied with a Gerlits–Nagy space, need not have Rothberger’s property. We apply these methods to construct a large family of spaces whose product with every Hurewicz space has Menger’s property. Our applications extend earlier results of Babinkostova and Scheepers.References
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Additional Information
- Boaz Tsaban
- Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
- MR Author ID: 632515
- Email: tsaban@math.biu.ac.il
- Lyubomyr Zdomskyy
- Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, 1090 Vienna, Austria
- MR Author ID: 742789
- Email: lzdomsky@logic.univie.ac.at
- Received by editor(s): May 30, 2012
- Received by editor(s) in revised form: September 8, 2012
- Published electronically: May 2, 2014
- Communicated by: Julia Knight
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 2881-2890
- MSC (2010): Primary 03E17, 26A03, 03E75
- DOI: https://doi.org/10.1090/S0002-9939-2014-12012-0
- MathSciNet review: 3209341