无限的形状
The Shape of Infinity
摘要：
在这些临时笔记中，针对没有点集拓扑背景的学生，我们在不涉及开集、闭集、滤子或网的情况下发展了斯通-切赫紧化的基本理论。特别地，这意味着我们不能使用任何通常的拓扑空间定义。这可能看起来像是提议单脚跳着跑马拉松，但它比看起来容易，而且并不缺乏兴趣。我们使用规范空间（一致空间提出了一个家庭的伪度量）;我们定义为总有界性加上完整性的紧凑性;我们定义完整性使用的变化Lawvere的分类表征的完整性度量空间。
英文摘要：
In these expository notes, intended for students without background in point-set topology, we develop the basic theory of the Stone-Cech compactification without reference to open sets, closed sets, filters, or nets. In particular, this means we cannot use any of the usual definitions of topological space. This may seem like proposing to run a marathon while hopping on one foot, but it is easier than it may appear, and not devoid of interest. We use gauge spaces (uniform spaces presented by a family of pseudometrics); we define compactness as total boundedness plus completeness; and we define completeness using a variation on Lawvere's categorical characterization of completeness for metric spaces.
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。
