Let $X$ be a real normed vector space. Let $A, B \subset X$ be nonempty, disjoint convex sets with $A$ compact and $B$ closed. Then there exist $f \in X^*$ and real numbers $\alpha_1 < \alpha_2$ such that
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\begin{align*}
f(a) \le \alpha_1 < \alpha_2 \le f(b) \quad \text{for all } a \in A, \; b \in B.
\end{align*}