论文标题
通过邻接空间的非Hausdorff歧管
Non-Hausdorff Manifolds via Adjunction Spaces
论文作者
论文摘要
在本文中，我们将介绍和发展一个辅助空间理论，该理论允许从标准Hausdorff的非Hausdorff拓扑歧管构建。这是通过沿同质形态开放式子曼菲尔德粘合豪斯多夫歧管的同时将这些地区的界限粘合而来的。在这些胶合区具有同型界限的情况下，据表明，侵犯豪斯多夫的行为正是在这些边界处发生的。然后，我们使用这种辅助形式主义来提供对给定的非Hausdorff歧管可能承认的最大Hausdorff submanifolds的部分表征。
In this paper we will introduce and develop a theory of adjunction spaces which allows the construction of non-Hausdorff topological manifolds from standard Hausdorff ones. This is done by gluing Hausdorff manifolds along homeomorphic open submanifolds whilst leaving the boundaries of these regions unidentified. In the case that these gluing regions have homeomorphic boundaries, it is shown that Hausdorff violation occurs precisely at these boundaries. We then use this adjunction formalism to provide a partial characterisation of the maximal Hausdorff submanifolds that a given non-Hausdorff manifold may admit.
