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
- J. Dieudonné (1966). "Sur la séparation des ensembles convexes". Math. Ann.. 163.
- 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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