Continuity properties of preference relations

Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient Conditions are given for in order-dense, strongly extensional preference relation on a complete metric space to be continuous. It is also shown, in the spirit of constructive reverse mathematics, that the continuity of sequentially continuous, order-dense preference relations on complete. separable metric spaces is connected to Ishihara's principle BD-N, and therefore is not provable within Bishop-style constructive mathematics alone. (C) WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim