Two types of fundamental spaces of differential forms on infinite dimensional topological vector spaces are considered; one is a fundamental space of Hida's type and the other is one of Malliavin's. It is proven that the former space is smaller than the latter. Moreover, it is shown that, under some conditions, the fundamental space of Hida's type is nuclear as a complete countably normed space, while that of Malliavin's in the L2 sense is not
