  We investigate the connection between the spatiality of locale products and
the earlier studies of the author on the locally fine coreflection of the
products of uniform spaces. After giving a historical introduction and
indicating the connection between spatiality and the locally fine construction,
we indicate how the earlier results directly solve the first of the two open
problems announced in the thesis of T. Plewe. Finally, we establish a general
isomorphism between the covering monoids of the localic product of topological
(completely regular) spaces and the locally fine coreflection of the
corresponding product of (fine) uniform spaces. Additionally, paper relates the
recent studies on formal topology and uniform spaces by showing how the
transitivity of covering relations corresponds to the locally fine
construction.
