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Radó's theorem (Riemann surfaces) : ウィキペディア英語版
Radó's theorem (Riemann surfaces)
In mathematical complex analysis, Radó's theorem, proved by , states that every connected Riemann surface is second-countable (has a countable base for its topology).
The Prüfer surface is an example of a surface with no countable base for the topology, so cannot have the structure of a Riemann surface.
The obvious analogue of Radó's theorem in higher dimensions is false: there are 2-dimensional connected complex manifolds that are not second-countable.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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