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.[1][2]
References[]
Categories:
- Convex analysis
- Theorems in functional analysis
- Topology stubs