%0 Journal Article
%T o-Boundedness of free topological groups
%A Taras Banakh
%A Du£¿an Repov£¿
%A Lyubomyr Zdomskyy
%J Mathematics
%D 2009
%I arXiv
%R 10.1016/j.topol.2009.10.006
%X Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group $F(X)$ over a Tychonov space $X$ is $o$-bounded if and only if every continuous metrizable image $T$ of $X$ satisfies the selection principle $U_{fin}(O,\Omega)$ (the latter means that for every sequence $<u_n>_{n\in w}$ of open covers of $T$ there exists a sequence $<v_n>_{n\in w}$ such that $v_n\in [u_n]^{<w}$ and for every $F\in [X]^{<w}$ there exists $n\in w$ with $F\subset\cup v_n$). This characterization gives a consistent answer to a problem posed by C. Hernandes, D. Robbie, and M. Tkachenko in 2000.
%U http://arxiv.org/abs/0904.1389v1