Continuity properties of preference relations
Marian Alexandru Baroni, Douglas Bridges · Mathematical logic quarterly · 2008
Abstract Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient conditions are given for an 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 principleBD‐ℕ, and therefore is not provable within Bishop‐style constructive mathematics alone. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)