树上的各种拓扑
Various topologies on trees
摘要：
这是一篇关于树的综述文章，其中有一些证明，可以有效地处理这些拓扑。树在集合论中被定义为偏序集合，其中每个元素下面的元素是良序的。一些不同的拓扑结构上的树木对待，有些在相当长的时间。有两个部分分别深入讨论粗楔形拓扑和细楔形拓扑以及区间拓扑。粗楔形拓扑给出了一类超紧单调正规拓扑空间，细楔形拓扑在每棵树上给出了一个单调正规的遗传超仿紧拓扑。区间拓扑给出了大量的拓扑性质，其中一些依赖于ZFC以外的集合论公理。在这一领域的许多开放的问题在最后一节中给出。
英文摘要：
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each element are well-ordered. A number of different topologies on trees are treated, some at considerable length. Two sections deal in some depth with the coarse and fine wedge topologies, and the interval topology, respectively. The coarse wedge topology gives a class of supercompact monotone normal topological spaces, and the fine wedge topology puts a monotone normal, hereditarily ultraparacompact topology on every tree. The interval topology gives a large variety of topological properties, some of which depend upon set-theoretic axioms beyond ZFC. Many of the open problems in this area are given in the last section.
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。
