  We continue the study of free Baxter algebras. There are two goals of this
paper. The first goal is to extend the construction of shuffle Baxter algebras
to completions of Baxter algebras. This process is motivated by a construction
of Cartier and is analogous to the process of completing a polynomial algebra
to obtain a power series algebra. However, as we will see later, unlike the
close similarity of properties of a polynomial algebra and a power series
algebra, properties of a shuffle Baxter algebra and its completion can be quite
different.
