摘要
我们开发一个理论向下，为 normed 的一个类的集合订了空格。在 normed 的 Westudy 最好的近似由元素订了空间 X 向下设定，并且为最好的近似的任何元素给必要、足够的条件由一向下关门了 X 的子集。我们也向下严格地描绘 X 的子集，并且证明那一向下 X 的子集严格地是向下如果并且仅当每它的边界点是 Chebyshev。获得的结果被用于一些 Chebyshev 对的检查(W， x ) ， x ∈ X 和 W 在此一向下关门了 X 的子集。
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X
