Description: Define the function associating with a set the free real vector space on
that set, equipped with the natural inner product and norm. This is the
direct sum of copies of the field of real numbers indexed by that set.
We call it here a "generalized real Euclidean space", but note that it
need not be complete (for instance if the given set is infinite
countable). (Contributed by Thierry Arnoux, 16-Jun-2019)