Conformal equivalence of countable dense sets
Conformal equivalence of countable dense sets
复制标题
可数稠密集的共形等价
DOI：
10.1090/s0002-9939-1967-0215994-8
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发表时间：
1967
期刊：
影响因子：
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通讯作者：
W. D. Maurer
中科院分区：
文献类型：
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作者：
W. D. Maurer
在[1，p.297，Problem 24]中，Erd6s问：“是否存在一个不是f(Z)=Ao+Aiz形式的整函数f，使得f(X)是有理的或无理的，因为x是有理的或无理的？更一般地，如果A和B是两个可数的稠密集合，是否存在将A映射到B的整函数？”下面的定理解决了这个问题的第二部分。
In [1, p. 297, problem 24], Erd6s asks: "Does there exist an entire functionf, not of the form f(z) = ao+aiz, such that the number f(x) is rational or irrational according as x is rational or irrational? More generally, if A and B are two denumerable, dense sets, does there exist an entire function which maps A onto B?" The following theorem settles the second part of this question as it is stated.