o-Boundedness of free topological groups

Details o-Boundedness of free topological groups o-Boundedness of free topological groups

2009-04-08

arxiv.org/abs/0904.1389v1

Topology and Its Applications 157:2 (2010), 466-481.

Mathematics

General Topology

24 pages, submitted

Scientific paper

10.1016/j.topol.2009.10.006

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]^{

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