Mathematical Sciences: Set-Theoretic Investigations on Classical Classes of Topological Spaces

正规拓扑空间的研究一直是经典集合论拓扑学中的一个重要课题，最近，正规局部紧Hausdorff空间的结构理论也引起了人们的关注。研究人员将研究几个众所周知的问题，主要涉及正规或正规局部紧空间类中的拓扑空间。在这些问题的最终解决中，集合论技术如强迫、无限组合和大基数将是主要的工具。集合论是数学的基础，因为所有的数学在原则上都可以从集合论建立起来，尽管需要费力地添加适当的定义，从选定的公理推导出结果，然后使用定义压缩它们的陈述。然而，一些主题更接近集合论，因为在这个过程中需要更少的附加定义。经典集合论拓扑学是这样一门学科，实际上是一个非常接近的学科，因此它分享了集合论本身的一些哲学重要性。

The study of normal topological spaces has long been an important topic in classical set-theoretic topology and, more recently, the structure theory of normal locally compact Hausdorff spaces has been of spacial interest. Several well- known problems, mostly involving topological spaces in the classes of normal or normal locally compact spaces, will be studied by the investigators. It is expected that set-theoretic techniques such as forcing, infinite combinatorics and large cardinals will be the principle tools used in the eventual solution of these problems. Set theory lies at the foundations of mathematics in that all of mathematics can in principle be built up from set theory, albeit laboriously, by adding appropriate definitions, deriving consequences from the chosen axioms, and then compressing their statements by use of the definitions. Some topics lie closer to set theory, however, by virtue of needing fewer added definitions in this process. Classical set-theoretic topology is such a subject, really a very close neighbor, and so it shares some of the philosophical importance of set theory itself.