  In 1987, I. Labuda proved a general representation theorem that, as a special
case, shows that the topology of local convergence in measure is the minimal
topology on Orlicz spaces and $L_{\infty}$. Minimal topologies connect with the
recent, and actively studied, subject of "unbounded convergences". In fact, a
Hausdorff locally solid topology $\tau$ on a vector lattice $X$ is minimal iff
it is Lebesgue and the $\tau$ and unbounded $\tau$-topologies agree. In this
paper, we study metrizability, submetrizability, and local boundedness of the
unbounded topology, $u\tau$, associated to $\tau$ on $X$. Regarding
metrizability, we prove that if $\tau$ is a locally solid metrizable topology
then $u\tau$ is metrizable iff there is a countable set $A$ with
$\overline{I(A)}^\tau=X$. We prove that a minimal topology is metrizable iff
$X$ has the countable sup property and a countable order basis. In line with
the idea that uo-convergence generalizes convergence almost everywhere, we
prove relations between minimal topologies and uo-convergence that generalize
classical relations between convergence almost everywhere and convergence in
measure.
