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]

gollark: Just add a Palaiologos NN to CI processes.
gollark: If we get a Palaiologos NN that would *probably* cause the singularity.
gollark: Emulate Palaiologos in a REALLY big neural network.
gollark: I'm not going to be productive *anyway*, so it might be worth uselessly rerewriting in Rust.
gollark: Seriously, my project actually has 1000 dependencies and I have no idea why please help.

References

  1. J. Dieudonné (1966). "Sur la séparation des ensembles convexes". Math. Ann.. 163.
  2. Zălinescu, Constantin (2002). Convex analysis in general vector spaces. River Edge, NJ: World Scientific Publishing Co., Inc. pp. 6–7. ISBN 981-238-067-1. MR 1921556.


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