Topological aspects of higher Baire space

真实的数的许多有趣的性质可以通过关注无理数来研究，并且在无理数和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性。最近的一个主要重点研究集理论一直在研究的推广，这与一些更大的地方设置的自然数。在这个研究项目中，学生将学习这种概括的拓扑方面-也就是说，理解它的“接近”的概念。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数学的其他领域的应用，例如模型论，在这些领域中，对自然数的关注是一个重要的限制。从那里的结果和一般的理解可能会流向意想不到的领域的应用。

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.