Dieudonné's theorem

Let $X$ be a locally convex space and $A,B\; \backslash subset\; X$ nonempty closed convex sets. If either $A$ or $B$ is locally compact and $\backslash operatorname\{recc\}(A)\; \backslash cap\; \backslash operatorname\{recc\}(B)$ (where $\backslash operatorname\{recc\}$ gives the recession cone) is a linear subspace, then $A\; -\; B$ is closed.{{cite journal|title=Sur la séparation des ensembles convexes|author=J. Dieudonné|year=1966|journal=Math. Ann.|volume=163|pages=1–3 |doi=10.1007/BF02052480 |s2cid=119742919 }}{{cite book |last=Zălinescu |first=Constantin |title=Convex analysis in general vector spaces |publisher=World Scientific Publishing Co., Inc. |isbn=981-238-067-1 |mr=1921556 |issue=J |year=2002 |location=River Edge, NJ |pages=6–7}}

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Category:Convex analysis

Category:Theorems in functional analysis

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