Applications of set theory to geometry and analysis

集合论在几何和分析中的应用

• 批准号: 8553-2006
• 负责人: Steprans, Juris
• 金额: $ 1.82万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2006
• 资助国家: 加拿大
• 起止时间: 2006-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=339632
• 关键词: Applications; set; theory; geometry; analysis

The question of the true nature of the geometric space in which we seem to live has been studied at least as far back as ancient Greece. Some of the modern answers to this problem require abandoning the common-sense continuum model and replacing it with discrete, computer like, models. One of the main goals of set theory is to examine the logical consequences of the continuum model and its implications for the rest of mathematical analysis. This proposal is about continuing this work with special emphasis on the notions of measure and invariance under geometric motions.

至少早在古希腊时期，人们就开始研究我们似乎所居住的几何空间的真实性质。这个问题的一些现代答案需要放弃常识连续模型，取而代之的是离散的、类似计算机的模型。集合论的主要目标之一是研究连续统模型的逻辑结果及其对其余数学分析的影响。这项提议是关于继续这项工作，特别强调几何运动下的测量和不变性的概念。