Summary: Let \(A\) be a subset in a locally convex space \(X\) and \(C\) be a closed convex cone with cusp condition. Denote by \(E(A\setminus C)\) the set of efficient points of the set \(A\) with respect to \(C\). Suppose that \(A\) is a compact \(F\)-set not necessarily convex. We obtain some results on the closedness of the set of efficient points. Furthermore, we prove that under some adequate convex assumptions the set \(S(A \setminus C)\) is connected.