关于压缩集与存在集的几点注记
Some remarks on contractive and existence sets
摘要：
设X是实或复巴拿赫空间，X中的F是非空集.称F为最佳共逼近存在集（简称存在集），如果对X中的任意x，$R_F(x)$不是空集，其中$$ R_F (x) = \{ d \in F : \|d-c\| \leq \|x-c\| \hbox{ for any } c \in F \}.$$显然，任何存在集都是X的压缩子集.本文的目的是给出F和X上存在集和压缩集概念等价的条件。
英文摘要：
Let X be a real or complex Banach space and let F in X be a non-empty set. F is called an existence set of best coapproximation (existence set for brevity), if for any x in X, $R_F(x)$ is not the empty set, where $$ R_F (x) = \{ d \in F : \|d-c\| \leq \|x-c\| \hbox{ for any } c \in F \}.$$ It is clear that any existence set is a contractive subset of X. The aim of this paper is to present some conditions on F and X under which the notions of exsistence set and contractive set are equivalent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
