A+ CATEGORY SCIENTIFIC UNIT

Non-separable Banach spaces with non-meager Hamel basis

Volume 189 / 2008

Taras Banakh, Mirna Džamonja, Lorenz Halbeisen Studia Mathematica 189 (2008), 27-34 MSC: 46B15, 03E75. DOI: 10.4064/sm189-1-3

Abstract

We show that an infinite-dimensional complete linear space $X$ has:

$\bullet$ a dense hereditarily Baire Hamel basis if $|X|\le{\mathfrak c}^+$;

$\bullet$ a dense non-meager Hamel basis if $|X|=\kappa^\omega=2^\kappa$ for some cardinal $\kappa$.

Authors

  • Taras BanakhInstytut Matematyki
    Uniwersytet Humanistyczno-Przyrodniczy
    im. Jana Kochanowskiego w Kielcach
    Świ/etokrzyska 15
    25-406 Kielce, Poland
    and
    Department of Mathematics
    Ivan Franko National University of Lviv
    1 Universytetska St.
    79000 Lviv, Ukraine
    e-mail
  • Mirna DžamonjaDepartment of Mathematics
    University of East Anglia
    Norwich, NR4 7TJ, United Kingdom
    e-mail
  • Lorenz HalbeisenTheoretische Informatik und Logik
    Universität Bern
    Neubrückstr. 10
    3012 Bern, Switzerland
    e-mail

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