In this talk I will introduce two spaces: the first space is
the usual n-dimensional vector space with the unusual feature that
n is a non-integer; the second space is composed of the linear
matrices acting on the previous space (physicists are particularly
interested in studying the limit as n goes to zero). These two
spaces are not known to most mathematicians, but they are
widely used by physicists. It is possible that, by extending the
notion of space, they can become well defined mathematical objects.