Some applications of set theory to measure theory and general topology

集合论在测度论和一般拓扑中的一些应用

• 批准号: 105396-2013
• 负责人: Burke, Maxim
• 金额: $ 0.8万
• 依托单位: University of Prince Edward Island
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=545131
• 关键词: Some; applications; set; theory; measure

My research focuses on general topology and measure theory. Some of the research has a set-theoretic flavor, as both of these areas occasionally require the use of deep set-theoretic techniques. The method of forcing especially, since 1963 when it was developed by Paul Cohen for proving that the Continuum Hypothesis is not decidable on the basis of the usual axioms for set theory, has led to important advances in these areas. One area dealt with in my proposal is measure theory, which is devoted to the study of methods for calculating lengths, areas and volumes and more general notions of a similar type. The problems that concern me have a set-theoretic flavor. Techniques from set theory have been successfully applied to similar problems in the past. One of the families of problems I am studying concerns the ability to approximate graphs of functions by graphs of smooth functions.

我的研究重点是一般拓扑和测度论。一些研究具有集合论的风格，因为这两个领域有时都需要使用深层集合论技术。尤其是自 1963 年 Paul Cohen 提出的强迫方法以来，它用于证明连续统假说在集合论的常用公理的基础上是不可判定的，这一方法在这些领域取得了重要进展。我的提案涉及的一个领域是测度论，它致力于研究计算长度、面积和体积的方法以及类似类型的更一般的概念。我关心的问题带有集合论的味道。集合论的技术过去已成功应用于类似的问题。我正在研究的一系列问题涉及通过平滑函数图来近似函数图的能力。