A remark on balls in normed linear spaces
D. Yost introduced the concept of the strong n-ball property for all integers \(n\geq 2.\) Definition. The subspace M of a normed linear space X is said to have the strong n-ball property if for any balls \(B_ 1,...,B_ n\) in X with \(\cap^{n}_{i=1}B_ i\neq \emptyset\) and \(B_ i\cup M\neq \emptyset\), \(i=1,...,n\), we have \(\cap^{n}_{i=1}B_ i\cup N\neq \emptyset.\) Yost asked whether the strong 3-ball property implies the strong n-ball property or not. In this paper the author proved: Theorem. Let M be a Chebyshev subspace in a real normed linear space X such that the unit ball of M has at least one extremal point and M has the strong 3-ball property, then M has the strong n-ball property for all n.
scientific article; zbMATH DE number 4060081