Continuous lexicographic preferences (Q2581788)

A binary relation representable as a lexicographic order on \(n\)-dimensional Euclidean space is considered. It is shown that a lexicographically representable binary relation has a continuous lexicographic representation if and only if it is locally utility representable. It is proved also that under some assumptions a binary relation with a lexicographic representation has a coordinate-continuous representation for \(n=2\).