The concept of demands introduced in Chapter 2 may be regarded as relations defined from the space of agents’ characteristics to the commodity space. From this perspective it is natural to be concerned with the mathematical properties of the relation including their continuity and measurability properties. Correspondingly, topological as well as measure theoretical structures in the universal preference set \( \mathcal{P} \) will be introduced in this chapter. It allows the space of agents’ characteristics, \( \mathcal{P} \) × \( \mathbb{G} \) , to be endowed with these structures. We then proceed to verify topological and measurable properties of demand relations.