Topology of the Efficient Sets of Convex Sets in $R^2$ Nguyen Quang Huy Abstract.      In this paper we prove that if a convex subset of $\Bbb R^2$ has compact sections with respect to the closure $\overline C$ of a convex cone $C$ (but the set itself may be noncompact) then its efficient set with respect to $C$ is homeomorphic to a polyhedral convex set, provided $\overline C$ is a pointed cone with nonempty interior.