Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 17 ноября 2014 г.
Аннотация:We study the question of the connectedness of suns in the space $ c_0$. We show that any sun $ M$ in $ c_0$ is m-connected (in the sense of Brown). It follows that $ M$ is monotonically path-connected and the intersection of $ M$ with an arbitrary ball in $ c_0$ is monotonically path-connected (and, in particular, path-connected). On the other hand, we establish that every approximatively compact m-connected set in $ c_0$ is a sun in $ c_0$. For $ X=c_0$, $ c$ or $ \ell^\infty$, it is proved that the intersection of a sun in $ X$ with a finite-dimensional coordinate subspace $ H_n\subset X$ is a $ P$-acyclic sun in $ H_n$.