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Q: Convergence of convex sets in the complementary Hausdorff metric and in the usual Hausdorff metric

BernsteinFirst of all let me define what is the the complementary Hausdorff distance between two open sets, I denoted by $d^{H}$ the usual Hausdorff distance in $\mathbb{R}^n$. Let $\Omega_1$ and $\Omega_2$ two open subsets of a (large) compact set $B \subset \mathbb{R}^n$, then their complementary Hau...

 

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