Smoothness of subspace sections of the unit balls of C(Q) and L^1статья
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Дата последнего поиска статьи во внешних источниках: 4 июня 2021 г.
Аннотация:We show that, for any integer , the space (where is a Hausdorff compact set, ) contains an -dimensional subspace such that any translation thereof by a vector , , intersects the unit ball of in a nonsmooth set. In , we show that if is an arbitrary finite-dimensional subspace in , , then there exists a dense set in the unit ball set of its translations that intersect the unit ball of in smooth sets. As an application, we show that in any finite-dimensional sun is convex. This extends the classical P. Ørno–Yu. A. Brudnyi–E. A. Gorin’s theorem to the effect that in any Chebyshev set is either a singleton or is infinite-dimensional.