...This property holds for any figure in the plane that is homeomorphic to a circle. "A figure in the plane that is homeomorphic to a circle divides the plane into two regions (Jordan's curve theorem)" is a fundamental theorem in plane topology. A figure in space that is homeomorphic to a circle does not divide the space in two. ... *Some of the terminology that refers to "Jordan's curve theorem" is listed below. Source | Heibonsha World Encyclopedia 2nd Edition | Information |
…この性質は,円と同相である平面上のどんな図形についても成立している。〈平面上における円と同相な図形は,平面を二つの領域に分ける(ジョルダンの曲線定理Jordan’s curve theorem)〉は平面位相幾何学における基本定理である。空間における円と同相な図形は空間を二分しない。… ※「Jordan's curve theorem」について言及している用語解説の一部を掲載しています。 出典|株式会社平凡社世界大百科事典 第2版について | 情報 |
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