Pareto efficiency without topology

Abstract Given a vector optimization problem over spaces endowed with topological linear structure, existence results for optima (efficient points) are known. Relying only on the set of properly efficient points from convex is proved to be nonempty and sets Proper Pareto coincide, provided that internal picked corresponding cone nonempty. This result appealing since scalarization valid without requirements. A As an important consequence, we provide Second Welfare Theorem in lattices especially Lebesgue holds topology.