Mathematical Sciences: Problems in Set-Theoretic Topology

数学科学：集合论拓扑问题

• 批准号: 8901931
• 负责人: Peter Nyikos
• 金额: $ 4.32万
• 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: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901931&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, the Continuum Hypothesis, Martin's Axiom, and the Proper Forcing Axiom), forcing techniques, inner model theory, and other set theoretic tools are used to clarify, and often solve, long-outstanding problems, and to isolate and identify topological properties worthy of study. The investigator will continue his research in this area. The research will focus on two primary topics and four secondary topics which show particular promise in the light of recent results by the investigator and others. The two primary topics are hereditary normality and sequential compactness, where it is hoped that recent successes with the topic of countable tightness can be extended and paralleled. The secondary topics are: locally compact spaces of small size, Frechet-Urysohn topological groups and vector spaces, nonmetrizable manifolds, and countable intersections of open sets in countably metacompact spaces.

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，连续统假设，马丁公理， 适当强迫公理），强迫技术，内部模型 理论和其他集合理论工具被用来澄清， 经常解决，长期悬而未决的问题，并孤立和 确定值得研究拓扑特性。 的 调查员将继续在这方面进行研究。 的 研究将集中在两个主要主题和四个次要主题上。 根据最近的情况， 研究者和其他人的结果。 两个主要议题 是遗传正规性和序列紧性，其中它是 我希望最近在可数紧度方面的成功 可以扩展和扩展。 次要主题是： 小尺寸局部紧空间，Frechet-Urysohn拓扑 群和向量空间，不可度量化流形，可数 可数亚紧空间中开集的交