In this work we characterize when a
single linear functional dominated by a sublinear functional
on a subspace of a real vector space has a unique extension to the
whole space dominated by
in terms of nested sequences of
``
-balls'' in a quotient space. This is then specialized to
obtain characterizations of the phenomenon when a single linear
functional on a subspace of a Banach space has unique
norm-preserving extension to the whole space, thus localizing and
generalizing some recent work of Oja and Põldvere. These results
are used to characterize
-asymptotic norming properties in
terms of nested sequences of balls in
extending the notion of
Property
introduced by Sullivan. A variety of examples and
applications of the main results are also presented.