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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== * * 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Radó's theorem (Riemann surfaces)」の詳細全文を読む スポンサード リンク
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