[1]毛超林.关于向量连续函数的一致逼近[J].深圳大学学报理工版,1986,(1):1-7.
 Mao Chaolin.On the Uniform Approximation of Vector Continuous Functions[J].Journal of Shenzhen University Science and Engineering,1986,(1):1-7.
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关于向量连续函数的一致逼近()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
期数:
1986年1期
页码:
1-7
栏目:
环境与能源
出版日期:
1986-03-31

文章信息/Info

Title:
On the Uniform Approximation of Vector Continuous Functions
作者:
毛超林
Author(s):
Mao Chaolin
文献标志码:
A
摘要:
        本文将Machado定理推广至紧集X上连续函数的任意集合.G.E.Silov[7]、 E. Bishop[1]、 Glicksberg[4]、D.Feyel 及 A. La Pradellew 等人运用反对称紧 集的概念,分别将Stone-Weierstrass定理成功地推广到子代数继而子空间最后凸子锥上.Machado151及Ransford[8]改进了 Bishop定理并简化其证明.1985年 4月,R.B.Burckel在一封给D.Feyel的信中,提出能否将Machado定理推广到[2]中情形的问题。
        本文肯定地回答了上述问题,并证明了Machado 定理一个非常广泛的特征,得到了包括上述所有结论的定理。
Abstract:
    This paper is an effort to generalize the Theorem of Machado to an arbitrary set of continuous functions on an compact X.
    G.E,Silov[7],E.Bishop[1],Glicksberg[4],D.FeyelandA. LePradelle[2] e already generalized successfully the Theorem of Stone-weierstrass to algebra, then to subspace and convex cone, utilizing the concept of antisymmetric compact. Machado[5] and then Ransford[8] have ameliorated result and simplified the proof of the Theorem of Bishop. In a letter to Feyel,R.B.Burckel raised the question whether the Theorem of Machado could be extended to the situation described in [2].
     This paper gives a positive reply to the above-mentioned question and proves the very general character of the Theorem of Mhcado,which leads to a theorem including all the results of the aforesaid authors.
更新日期/Last Update: 2016-05-23