论文标题
一维非Hausdorff歧管和平面的叶子
One dimensional non-Hausdorff manifolds and foliations of the plane
论文作者
论文摘要
最初的文章标题为“Variétés（NonSéparées）àuneDimension et Structuresfeuilletéesdu Plan”于1957年在法语中发表在L'EnseignementMathématique。它在飞机的叶子和非Hausdorff之间建立了美丽的联系，$ 1 $维歧管自然而然地作为叶子的叶子空间。自从出现以来，该理论为有关飞机的动态系统和叶子和$ 2 $ manifolds的几个结果铺平了道路。 Haefliger和Reeb的文章激发了许多成果的叶子理论，$ 3 $ - manifolds：我们将有兴趣的读者推荐给Danny Calegari关于该主题的书。 Haefliger和Reeb的文章也已应用于拓扑动态以外的区域。迄今为止，本文已在$ 43 $的论文中引用，并帮助建立了许多不错的结果。在文献中，本文的主要定理通常被称为Haefliger-reeb理论或“ Haefliger and Reeb的经典结果”。但是，据我们所知，目前尚无本文的英文版本。除了添加数字并纠正一些印刷错误外，我们已经使文章保持不变。我们希望这种翻译对更广泛的受众有用。
The original article titled "Variétés (non séparées) à une dimension et structures feuilletées du plan" was published in 1957 in French in L'Enseignement Mathématique. It establishes a beautiful connection between foliations of the plane and non-Hausdorff $1$-dimensional manifolds arising naturally as leaf spaces of the foliations. Since its appearance, this theory has paved the way for several results concerning dynamical systems and foliations of the plane and $2$-manifolds. Haefliger and Reeb's article inspires many results in the theory of foliation of $3$-manifolds as well: we refer the interested reader to Danny Calegari's book on the topic. Haefliger and Reeb's article also has been applied to areas outside topological dynamics. This article has been referenced in $43$ papers to-date and has helped build many nice results. In the literature, the main theorem of this article has been commonly referred to as Haefliger-Reeb theory or "a classical result by Haefliger and Reeb". However, to the best of our knowledge, no English version of this article is currently available. We have kept the article entirely unchanged except to add figures and correct a few typographical errors. We hope that this translation will be useful for the broader audience.
