  We study final group topologies and their relations to compactness
properties. In particular, we are interested in situations where a colimit or
direct limit is locally compact, a k_\omega-space, or locally k_\omega. As a
first application, we show that unitary forms of complex Kac-Moody groups can
be described as the colimit of an amalgam of subgroups (in the category of
Hausdorff topological groups, and the category of k_\omega-groups). Our second
application concerns Pontryagin duality theory for the classes of almost
metrizable topological abelian groups, resp., locally k_\omega topological
abelian groups, which are dual to each other. In particular, we explore the
relations between countable projective limits of almost metrizable abelian
groups and countable direct limits of locally k_\omega abelian groups.
