  As a generalization of almost everywhere convergence to vector lattices,
unbounded order convergence has garnered much attention. The concept of
boundedly uo-complete Banach lattices was introduced by N. Gao and F. Xanthos,
and has been studied in recent papers by D. Leung, V.G. Troitsky, and the
aforementioned authors. We will prove that a Banach lattice is boundedly
uo-complete iff it is monotonically complete. Afterwards, we study
completeness-type properties of minimal topologies; minimal topologies are
exactly the Hausdorff locally solid topologies in which uo-convergence implies
topological convergence.
