Given a choice problem, the maximization rule may select many alternatives. In such cases, it is common practice to interpret that the final choice will end up being made by some random procedure, assigning to any maximal alternative the same probability of being chosen. However, there may be...

In this paper we begin the investigation of filters and congruences. We define the filters of a pseudo BL-algebra A and we denote by F(A) ()(AFn) lattice of all filters (normal filters) of A; we put in evidence some results about these lattices. By using the two distance functions we define two...

This paper generalizes two theorems in Campbell and Walker (1990), which is based on weak upper continuity. A new property, called partial upper continuity, is shown to be sufficient for representation and existence of a maximal element. Noting that transfer weak upper continuity (Tian and Zhou,...

I revisit thoroughly the standard boundary behavior satisfied by the excess demand function of a competitive economy, and I prove two implications of the boundary behavior. Then, I show that these implications lead to an alternative proof of the existence of competitive equilibria which is...