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.
"Uniform Continuity Properties of Preference Relations." Notre Dame J. Formal Logic 49 (1) 97 - 106, 2008. https://doi.org/10.1215/00294527-2007-006