Dieudonné's theorem

In mathematics, Dieudonné's theorem, named after Jean Dieudonné, is a theorem on when the Minkowski sum of closed sets is closed.

Statement

Let $X$ be a locally convex space and $A,B\subset X$ nonempty closed convex sets. If either $A$ or $B$ is locally compact and $\operatorname {recc} (A)\cap \operatorname {recc} (B)$ (where $\operatorname {recc}$ gives the recession cone) is a linear subspace, then $A-B$ is closed.