It was shown in previous papers
[C. T. Tucker, “Homomorphisms of Riesz spaces,” Pacific J. Math., 55 (1974),
289–300, and “Concerning σ-homomorphisms of Riesz spaces,” Pacific J. Math., 57
(1975), 585–590] that there is a large class β of Riesz spaces with the property that if
L belongs to β and ϕ is a Riesz homomorphism of L into an Archimedean Riesz
space then ϕ preserves the order limit of sequences. In this paper it is shown
that if L belongs to β then every order bounded linear map of L into an
Archimedean, directed, partially ordered vector space is sequentially continuous. An
application of this is made to the theory of Baire funtions. Further, some
properties of those members of β which are also normed Riesz spaces are
considered.
