Ball-Complete Sets and Solar Properties of Sets in Asymmetric Spacesстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 1 апреля 2022 г.
Аннотация:Several important classical concepts and problems of geometric approximation theory are extended to asymmetric spaces. We introduce the concept of B˚-complete (ball-complete) sets and show that the class of such sets is equal to the class of unimodal sets. For symmetrizable asymmetric reflexive locally uniformly convex spaces, we prove that the class of closed B˚-connected sets (such sets have connected intersections with open balls) coincides with the class of unimodal sets. For smooth spaces, we show that any closed almost sun is convex. We also examine some categorical properties of points of existence and approximative compactness in asymmetric spaces