  Early this century K. H. Hofmann and S. A. Morris introduced the class of
pro-Lie groups which consists of projective limits of finite-dimensional Lie
groups and proved that it contains all compact groups, all locally compact
abelian groups, and all connected locally compact groups and is closed under
the formation of products and closed subgroups. They defined a topological
group $G$ to be almost connected if the quotient group of $G$ by the connected
component of its identity is compact.
  We show here that all almost connected pro-Lie groups as well as their
continuous homomorphic images are $R$-factorizable and
\textit{$\omega$-cellular}, i.e.~every family of $G_\delta$-sets contains a
countable subfamily whose union is dense in the union of the whole family. We
also prove a general result which implies as a special case that if a
topological group $G$ contains a compact invariant subgroup $K$ such that the
quotient group $G/K$ is an almost connected pro-Lie group, then $G$ is
$R$-factorizable and $\omega$-cellular.
  Applying the aforementioned result we show that the sequential closure and
the closure of an arbitrary $G_{\delta,\Sigma}$-set in an almost connected
pro-Lie group $H$ coincide.
