Dieudonné's theorem - Alchetron, The Free Social Encyclopedia

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

Statement of theorem

Let nonempty closed convex sets A , B ⊂ X a locally convex space, if either A or B is locally compact and recc ⁡ ( A ) ∩ recc ⁡ ( B ) (where recc gives the recession cone) is a linear subspace, then A − B is closed.

References

Dieudonné's theorem Wikipedia

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