Mathematical Sciences: Problems in Set-Theoretic Topology

数学科学：集合论拓扑问题

• 批准号: 8703008
• 负责人: Peter Nyikos
• 金额: $ 3.63万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703008&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Set; Theoretic

Set-theoretic topology is a branch of topology in which set- theoretic techniques are used to solve problems about abstract spaces. In it, special axioms (such as Godel's Axiom of Constructibility, Martin's Axiom, the covering Lemma, and the Product Measure Extension Axiom), forcing techniques, and other set-theoretic tools are used to clarify, and often solve, long- outstanding problems, and through consistency results to isolate and identify topological properties worthy of study. The principal investigator will continue his research in this branch, centered on four areas where recent results have greatly enhanced our understanding of the spaces in question and, in some cases, the set-theoretic tools themselves. The spaces in question are various classes of countably compact spaces; Frechet chain net spaces; nonmetrizable manifolds; and countably metacompact spaces. Such studies will probably have less immediate application than more geometric topological studies but in the long run can be expected to influence our ideas about space and even about the nature of proof.

集论拓扑是拓扑学的一个分支，其中集- 理论技术用于解决抽象问题， 空间. 其中，特殊公理（如哥德尔公理） 可构造性，马丁公理，覆盖引理， 乘积测度扩展公理）、强迫技术和其他 集合论工具被用来澄清，并经常解决，长期- 突出问题，并通过一致性结果来隔离 并确定值得研究的拓扑性质。 的 首席研究员将继续他在这个分支的研究， 集中在四个领域，最近的成果大大提高了 我们对空间的理解，在某些情况下， 集合论工具本身。 有问题的空间是 各种可数紧空间;弗雷歇链网 空间;不可度量化流形;可数亚紧 空间. 这样的研究可能不会那么直接 应用比更多的几何拓扑研究，但在 从长远来看，可以预期会影响我们对太空的看法， 甚至是关于证据的本质