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

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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.