  In this note, we give several definitions of metric corona properties which
could be of interest in Set Topology, Functional Analysis and Approximation
Theory, and prove that there are complete metrizable t.v.s. which are nice in
the sense that they have a metric which is invariant by translations, but they
do not have good corona properties. All classical function spaces satisfy good
corona properties but it is an open question to know if this also holds for the
more general setting of locally convex t.v.s.
