Two spaces looking for a geometer

In this talk I will introduce two spaces: the prst 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 de�ned mathematical objects.