Let H={0, 1/2, 1} with the natural order and p&q= max{p+ q- 1, 0} for all p, q is an element of H. We know that the category of liminf complete H-ordered sets is Cartesian closed. In this paper, it is proved that the category of conically cocomplete H-ordered sets with liminf continuous functions as morphisms is Cartesian closed. More importantly, a counterexample is given, which shows that the function spaces consisting of liminf continuous functions of complete H-ordered sets need not be complete. Thus, the category of complete H-ordered sets with liminf continuous functions as morphisms is not Cartesian closed. (c) 2020 Elsevier B.V. All rights reserved
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