有界实值函数空间中的一致逼近

Uniform Approximation in the Space of Real-valued Bounded Functions

本文研究定义在任意点集X上的有界实值函数空间B(X)中的一致逼近问题,证明了B(X)中S_1太阳集的内在特征是具弱中间性质;同时给出了B(X)中最佳一致逼近的Kolmogorov特征定理;最后作为直接的推论,给出几个常用的空间如C_b(X),C(X)及l~∞(Γ)中相应的结论。

In this paper, the author studies the uniform approximation in B(X)——the space of real-valued bounded functions defined on an arbitrary set X. It is proved that S_1 sun, in B(X) is with an intrinsic feature of weak betweenness property. Then, the author gives the Kolmogorov characterization of the best approximation in B(X). As direct corollaries, the author finally gives relevant conclusions in several useful spaces as C_b(X), C(X), and l~∞(P).