Continuously representable Paretian quasi-orders (Q850469)

This article investigates relations between topologies defined employing Pareto order relations, establishing conditions for continuity of Pareto representations. Taking in the domain the Pareto order topology, conditions are determined for continuity as the image is endowed with the Pareto Topology and, alternatively, for coordinate-continuity. The conditions for the existence of continuous representations are, in the first case, that all indifference sets are open in the Pareto order topology and, in the second case, that this holds for the incomparability sets.