Solarity of Chebyshev sets in dual spaces and uniquely remotal Setsстатья
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Дата последнего поиска статьи во внешних источниках: 15 июля 2021 г.
Аннотация:Two max- and min-approximation problems on solarity of sets in dual spaces are considered. It is shown that if the metric projection onto a set M⊂X∗ is w∗-upper semicontinuous and has nonempty w∗-closed acyclic values, then M is a sun. In particular, a Chebyshev set with w∗-continuous metric projection is a sun. In the max-approximation setting, a set with w∗-upper-semicontinuous max-projection with nonempty w∗-closed acyclic values is shown to be local max-sun. As a result, it follows that that a uniquely remotal set with w∗-continuous max-projection operator is a singleton, which gives an answer to the well-known unique farthest point problem in dual spaces for sets with w∗-continuous farthest-point mapping.