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Дата последнего поиска статьи во внешних источниках: 26 июня 2019 г.
Аннотация:A~direction $d$ is called a~tangent direction to the unit sphere~$S$ if the conditions
$s\in S$ and $\operatorname{aff}(s+d)$ is a~tangent line to the sphere~$S$ at~$s$ imply that
$\operatorname{aff}(s+d)$ is a~one-sided tangent to the sphere~$S$, i.e., it is the limit of
secant lines at the point~$s$. A~set~$M$ is said to be convex with respect to a~direction~$d$ if
$[x,y]\subset M$ whenever $x,y\in M$, $(y-x)\parallel d$. It is shown that in an arbitrary normed space an arbitrary sun (in particular, a~boundedly compact Chebyshev set) is convex with respect to any tangent direction of the unit sphere.