The notion of ball proximinality and the strong ball proximinality were recently introduced in [2]. We prove that an equable subspaceY of a Banach spaceX is strongly ball proximinal and the metric projection fromX, onto the closed unit ball ofY, is Hausdorff metric continuous.

中文翻译：

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等距球的球近性

最近在[2]中引入了球邻近性和强球邻近性的概念。我们证明Banach空间X的一个相等的子空间Y是球的近邻，并且从X到Y的闭合单位球的度量投影是Hausdorff度量连续的。