On the Inexistence of Additive Equi-Lipschitzian Parametrizations of Compact Convex Subsets
Tóm tắt
A Banach space of dimension at least 2 does not admit an equi-Lipschitzian family of additive mappings parametrizing all non-empty compact convex sets. Examples of linear Lipschitzian as well as positively homogeneous equi-Lipschitzian parametrizations exist in the literature.
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