Topological properties of spaces ordered by preferences (Q1283396)

A preference on a set is an asymmetric, negatively transitive binary relation on it. The author studies spaces ordered by preferences. These are triples \((X,<,\tau)\) where \(<\) is a preference on \(X\) and \(\tau\) is a topology on \(X\) such that the order topology \(\leq \tau\) and \(\tau\) has a base formed by convex sets. In particular he shows that they are monotonically normal, hereditarily normal, completely regular and hereditarily collectionwise normal.