# zbMATH — the first resource for mathematics

Uniform continuity properties of preference relations. (English) Zbl 1186.03074
The anti-Specker property, a constructive version of sequential compactness, is used to prove constructively that a pointwise continuous, order-dense preference relation on a compact metric space is uniformly sequentially continuous. It is then shown that Ishihara’s principle BD-N implies that a uniformly sequentially continuous, order-dense preference relation on a separable metric space is uniformly continuous. Converses of these two theorems are also proved.

##### MSC:
 03F60 Constructive and recursive analysis 91B08 Individual preferences
##### Keywords:
constructive mathematics; preference relation; continuity