Sul prodotto tensoriale di una infinità di K-spazi vettoriali

All infinite families F of K-vector spaces with the following properties are determinated: the dimension of the tensor product of all V ∈ F is equal of the product of the dimensions of all V and, choosing a basis in any V, the tensor mapping maps the product of these basis into a basis of the tensor product. Moreover, a characterization, which is formally equal to that the universal tensor product property, is given for the K-vector space with dimension equal to the product of an arbitrary family di fixed cardinal numbers.