We introduce three new classes of ordered topological vector spaces and investigate some of their properties. We show that they are good enough for the validity of the analogues of the Banach-Steinhaus theorem for sets of positive linear mappings, and this helps us obtain some results about positive Schauder bases. We use to advantage one of these classes of spaces to give an affirmative answer to a question raised in ([35]) about the order-bounded sets in the tensor products of ordered locally convex spaces. We prove some results on the continuity of sublinear mappings of ordered vector spaces equipped with the order bound sc-topology (see the text for the definition). Finally, we prove a type of closed graph theorem for ordered topological abelian groups.

Doctor of Philosophy (PhD)