Theorema Dieudonnéanum Propositum theorematis | Notae | Tabula navigationisAmplifica

Theoremata mathematica


Ioanne Dieudonnémathematicatheoremasumma Minkowskianacopiarum clausarumcopiisspatium localiter convexumlocaliter sit compactumconum recessionissubspatium lineare




Theorema Dieudonnéanum, ex Ioanne Dieudonné appellatum, in mathematica est theorema de casu ubi summa Minkowskiana copiarum clausarum clauditur.



Propositum theorematis |


Datis copiis convexis clausis non vacuis A,B⊂Xdisplaystyle A,Bsubset X, spatium localiter convexum, si aut Adisplaystyle A aut Bdisplaystyle B localiter sit compactum et recc⁡(A)∩recc⁡(B)displaystyle operatorname recc (A)cap operatorname recc (B) (ubi reccdisplaystyle operatorname recc conum recessionis dat) sit subspatium lineare, tum A−Bdisplaystyle A-B clauditur.[1][2]



Notae |



  1. ↑ Jean Dieudonné (1966). "Sur la séparation des ensembles convexes". Mathematische Annalen 163 .


  2. ↑ Constantin Zălinescu, Convex Analysis in General Vector Spaces (River Edge, Novae Caesareae: World Scientific Publishing, 2002), pp. 6–7. ISBN 981-238-067-1. MR 1921556.


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