经由伴随空间的非Hausdorff流形
Non-Hausdorff Manifolds via Adjunction Spaces
摘要：
在本文中，我们将介绍和发展的理论，允许建设非豪斯多夫拓扑流形从标准的豪斯多夫。这是通过沿着同胚开子流形粘合豪斯多夫流形而不确定这些区域的边界来完成的。在这种情况下，这些胶合区域同胚的边界，它表明，豪斯多夫违反恰好发生在这些边界。然后，我们使用这种附加形式主义提供一个部分的最大豪斯多夫子流形，一个给定的非豪斯多夫流形可能承认的特征。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
