The classical Uryson-Titze theorem states that every continuous function defined on a closed subset of a normal topological space can be extended to the whole space. However, not every continuous and monotone function defined on a closed subset of a normally preordered space is extendable to the...

This paper studies the existence of Pareto optimal, envy-free allocations of a heterogeneous, divisible commodity for a finite number of individuals. We model the commodity as a measurable space and make no convexity assumptions on the preferences of individuals. We show that if the utility...