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  • Scales, fields, and a problem of Hurewicz
    Tsaban, Boaz ; Zdomskyy, Lyubomyr
    Menger's basis property is a generalization of ▫$\sigma$▫-compactness and admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct ... non-▫$\sigma$▫-compact sets of reals with Menger's property. Special instances of these constructions give known counterexamples to conjectures of Menger and Hurewicz. We obtain the first explicit solution to the Hurewicz 1927 problem, that was previously solved by Chaber and Pol on a dichotomic basis. The constructed sets generate nontrivial subfields of the real line with strong combinatorial properties, and most of our results can be stated in a Ramsey-theoretic manner. Since we believe that this paper is of interest to a diverse mathematical audience, we have made a special effort to make it self-contained and accessible.
    Source: Journal of the European Mathematical Society. - ISSN 1435-9855 (Vol. 10, iss. 3, 2008, str. 837-866)
    Type of material - article, component part
    Publish date - 2008
    Language - english
    COBISS.SI-ID - 16356953

    Link(s):

    http://dx.doi.org/10.4171/JEMS/132

source: Journal of the European Mathematical Society. - ISSN 1435-9855 (Vol. 10, iss. 3, 2008, str. 837-866)

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