论文标题
在次数规范的空间中最近的点问题
Nearest point problem in countably normed spaces
论文作者
论文摘要
在一个符合规范的空间中，该空间是一个线性空间，配备了可计数的配对兼容规范，如果此子集相对于所有规范，我们从非空分之外的一个点证明了一个公共最近的点（在所有规范中）。如果仅配备了其规范之一的空间的完成是统一的，我们还证明了该共同点的独特性。
In a countably normed space which is a linear space equipped with a countable number of pair-wise compatible norms, we prove the existence of a common nearest point (in all norms) from a point outside a nonempty subset if this subset is compact with respect to all norms. We also prove the uniqueness of that common nearest point if the completion of the space equipped with only one of its norms is uniformly convex.
