o-Boundedness of free topological groups

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 $_{n\in w}$ of open covers of $T$ there exists a sequence $_{n\in w}$ such that $v_n\in [u_n]^{