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Ordered locally convex spaces is an important classes of spaces in the theoryof ordered topological vector spaces just as locally convex spaces in thetheory of topological vector spaces. Some special classes of ordered locallyconvex spaces such as order infrabarrelled spaces have been studied. Thepurpose of this paper is to initiate the study of order bornological spaces andtheir fundamental properties. In addition, order ultrabornological spaces isalso investigated as an important special class of order bornological spaces.

Order bornological spaces and order ultrabornological spaces