Topological aspects of higher Baire space

高贝尔空间的拓扑方面

• 批准号: 2594815
• 金额: --
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2594815
• 关键词: Topological; aspects; higher; Baire; space

Many interesting properties of the real numbers can be studied by focusing attention on the irrational numbers, and there is a convenient equivalence between the irrationals and the set of all functions from natural numbers to natural numbers. A recent major focus of research in set theory has been in studying a generalisation of this, with some larger set taking the place of the natural numbers. In this research project the student will study topological aspects of this generalisation - that is, understanding it in terms of a notion of "closeness". As well as the intrinsic interest in understanding this natural mathematical structure, the research may lead to applications in other areas of mathematics such as model theory, where constraining attention to the natural numbers is a significant restriction. From there results and general understanding may flow on to applications in unexpected areas.

关注无理数可以研究实数的许多有趣的性质，无理数与从自然数到自然数的所有函数的集合之间有一个方便的等价关系。集合论最近的一个主要研究重点是研究这一点的推广，用一些更大的集合来取代自然数。在这个研究项目中，学生将学习这一概括的拓扑学方面--也就是说，用一个“密切”的概念来理解它。除了对理解这种自然数学结构的内在兴趣之外，这项研究还可能导致在其他数学领域的应用，如模型理论，在这些领域，限制对自然数的关注是一个重要的限制。从这些结果和一般理解可能会流到意想不到的领域的应用。