  Ordered locally convex spaces is an important classes of spaces in the theory
of ordered topological vector spaces just as locally convex spaces in the
theory of topological vector spaces. Some special classes of ordered locally
convex spaces such as order infrabarrelled spaces have been studied. The
purpose of this paper is to initiate the study of order bornological spaces and
their fundamental properties. In addition, order ultrabornological spaces is
also investigated as an important special class of order bornological spaces.
