Abstract
A Minkowski–Rådström–Hörmander space is a quotient space over the family
of all non-empty bounded closed convex subsets of a Banach space
We prove in Theorem 4.2 that a metric
(Bartels–Pallaschke metric) is the strongest of all complete metrics in the cone
and Hausdorff metric
is the coarsest of them. Our results follow from Theorem 3.1 for the more general case of a quotient space over an abstract convex cone
with complete metric
. We also extend a definition of Demyanov’s difference (related to Clarke’s subdifferential) of finite-dimensional convex sets
to infinite dimensional Banach space
and we prove in Theorem 4.1 that Demyanov’s metric generated by such extension, is complete.