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.