| 词条 | Radó's theorem (Riemann surfaces) |
| 释义 |
In mathematical complex analysis, Radó's theorem, proved by {{harvs|txt|first=Tibor|last=Radó|authorlink=Tibor Radó|year=1925}}, 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
2 : Riemann surfaces|Theorems in complex analysis |
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