  We show that any metacompact Moore space is monotonically metacompact and use
that result to characterize monotone metacompactness in certain generalized
ordered (GO)spaces. We show, for example, that a generalized ordered space with
a sigma-closed-discrete dense subset is metrizable if and only if it is
monotonically (countably) metacompact, that a monotonically (countably)
metacompact GO-space is hereditarily paracompact, and that a locally countably
compact GO-space is metrizable if and only if it is monotonically (countably)
metacompact. We give an example of a non-metrizable LOTS that is monotonically
metacompact, thereby answering a question posed by S. G. Popvassilev. We also
give consistent examples showing that if there is a Souslin line, then there is
one Souslin line that is monotonically countable metacompact, and another
Souslin line that is not monotonically countably metacompact.
