  We show that under a separation property, a $\mathcal{Q}$-minimal point in a
normed space is the minimum of a given sublinear function. This fact provides
sufficient conditions, via scalarization, for nine types of proper efficient
points; establishing a characterization in the particular case of Benson proper
efficient points. We also obtain necessary and sufficient conditions in terms
of scalarization for approximate Benson and Henig proper efficient points. The
separation property we handle is a variation of another known property and our
scalarization results do not require convexity or boundedness assumptions.
