# Dieudonné's theorem

Let nonempty closed convex sets ${\displaystyle A,B\subset X}$ a locally convex space, if either ${\displaystyle A}$ or ${\displaystyle B}$ is locally compact and ${\displaystyle \operatorname {recc} (A)\cap \operatorname {recc} (B)}$ (where ${\displaystyle \operatorname {recc} }$ gives the recession cone) is a linear subspace, then ${\displaystyle A-B}$ is closed.[1][2]