We can extend the Banach-Mazur distance to be a distance between non-symmetric sets by allowing affine transformations instead of linear transformations. It was proved in [J] that for every convex bodyK we haved(K, D)≤n. It is proved that ifK is a convex body in ℝn such thatd(K, D)=n, thenK is a simplex.
Convex Body Common Point Affine Transformation Subsidiary Condition Symmetric Convex
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