  In this paper, the continuity and strong continuity in domain-free
information algebras and labeled information algebras are introduced
respectively. A more general concept of continuous function which is defined
between two domain-free continuous information algebras is presented. It is
shown that, with the operations combination and focusing, the set of all
continuous functions between two domain-free s-continuous information algebras
forms a new s-continuous information algebra. By studying the relationship
between domain-free information algebras and labeled information algebras, it
is demonstrated that they do correspond to each other on s-compactness.
