无理数上的等距嵌入和连续映射
Isometric embeddings and continuous maps onto the irrationals
摘要：
设f是完备可分度量空间E到无理数上的连续映射。证明了如果完备可分度量空间M包含E中每个闭相对离散集的等距拷贝，则M也包含f的某个纤维的等距拷贝.我们还将证明，如果f的所有纤维都有正维数，则E中的零维闭集的集合在E的Wijsman超空间中是非解析的。
英文摘要：
Let f be a continuous map of a complete separable metric space E onto the irrationals. We show that if a complete separable metric space M contains isometric copies of every closed relatively discrete set in E, then M contains also an isometric copy of some fiber of f. We shall show also that if all fibers of f have positive dimension, then the collection of closed zero-dimensional sets in E is non-analytic in the Wijsman hyperspace of E.
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。
