序空间、度量原像与函数代数
Ordered Spaces, Metric Preimages, and Function Algebras
摘要：
我们考虑复斯通-维尔斯特拉斯性质（CSWP），这是斯通-维尔斯特拉斯定理的复版本。若X是三个线性序空间的乘积的紧致子空间，则X有CSWP当且仅当X没有子空间同胚于康托尔集。此外，双箭空间的每个有限方幂都有CSWP。这些结果是利用在紧度量空间上具有离散到一映射的紧T2空间的一些结果得到的.
英文摘要：
We consider the Complex Stone-Weierstrass Property (CSWP), which is the complex version of the Stone-Weierstrass Theorem. If X is a compact subspace of a product of three linearly ordered spaces, then X has the CSWP if and only if X has no subspace homeomorphic to the Cantor set. In addition, every finite power of the double arrow space has the CSWP. These results are proved using some results about those compact Hausdorff spaces which have scattered-to-one maps onto compact metric spaces.
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