Consider the sets ##X:= \{x\in\mathbb R^2: \enspace ||x-(-1,0)||_2 \leq 1\}## (a ball) and ##Y:=co\{(0,-1), (0,1), (1,0)\}## (a triangle).(adsbygoogle = window.adsbygoogle || []).push({});

Both ##X## and ##Y## are compact and convex, but they aren't disjoint: ##X\cap Y = \{(0,0)\}##. Since they aren't disjoint, the most common separating hyperplane/Hahn-Banach theorems don't directly apply. However, the y-axis is a hyperplane which separates them in a weak sense.

Can anybody point me to source for a separating hyperplane theorem that covers this example? Ideally, I'm looking for something that isn't restricted to finite dimensions.

Thanks!

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# Separating hyperplane theorem for non-disjoint sets

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