In this paper, X denotes a Hausdorff paracompact locally compact space, E a Hausdorff locally convex space over K, the field of real or complex numbers (we call the elements of K scalars), a filtering upwards family of semi-norms on E generating the topology of E, Cb(X) the space of all continuous scalar-valued funcions on X, and Cb(X, E) the space of all continuous, bounded E-valued functions.

In this paper the representation type of the class of pointed irreducible coalgebras is studied. We refer the reader to [4] for the basic definitions. A coalgebra is of bounded representation type if there is a bound on the dimension of finite dimensional indecomposable comodules. In Section 1, we show that the representation type is dependent upon the size of the space of primitives. Indeed, a pointed irreducible coalgebra is of bounded type if and only if it is finite dimensional and the space of primitives is onedimensional, i.e. if and only if it is a coalgebra spanned by a finite sequence of divided powers.