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  be a locally convex space and  nonempty closed convex sets. If either  or  is locally compact and  (where  gives the recession cone) is a linear subspace, then  is closed.

References 

Convex analysis
Theorems in functional analysis