Non-separable Banach spaces with non-meager Hamel basis
Volume 189 / 2008
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 $\kappa$.
