不通过识别点来粘合空间
Glueing spaces without identifying points
AI总结：
本文发展Artin-Wraith粘合理论，证明粗空间的紧化范畴在粗等价下不变，并推广端空间性质，还证明Cantor集去点紧化的唯一性。
摘要：
本文发展了拓扑空间的Artin-Wraith粘合理论。作为应用，我们证明了某些与粗结构一致的粗空间的紧化范畴在粗等价下不变。因此，如果X和Y是某些粗等价的行为良好的度量空间，则它们具有相同的端空间（推广了适用于拟等距真测地度量空间的众所周知的事实）。作为另一个应用，我们证明对于每个紧致可度量化空间Y，至多存在一个（在同胚意义下）Cantor集去掉一点后的紧化，使得其余空间同胚于Y。
英文摘要：
In this paper we develop the theory of Artin-Wraith glueings for topological spaces. As an application, we show that some categories of compactifications of coarse spaces that agree with the coarse structures are invariant under coarse equivalences. As a consequence, if X and Y are some well behaved metric spaces that are coarse equivalent, then they have the same space of ends (generalizing the well known fact that works on quasi-isometric proper geodesic metric spaces). As another application, we show that for every compact metrizable space $Y$, there exists only one, up to homeomorphisms, compactification of the Cantor set minus one point such that the remainder is homeomorphic to $Y$.
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。
