Production equilibria in vector lattices with unordered preferences : an approach using finite-dimensional approximations

The goal of the paper is to prove the existence of competitive production quasi-equilibria in linear vector lattices. We assume that the commodity space is a vector lattice endowed with a Hausdorff locally convex topology such that the positive cone is closed and the topological dual is a lattice. Preferences are not assumed to be transitive and complete. We allow also a rather arbitrary form of consumption sets which, together with production sets, satisfy a kind of proper condition. This condition "a set to be proper" is significantly weakened in comparison with other papers. The existence result is stated via the method of finite-dimensional approximations of the commodity space.