On the complexity of subspaces of
Carlos Uzcátegui (2003)
Fundamenta Mathematicae
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Let (X,τ) be a countable topological space. We say that τ is an analytic (resp. Borel) topology if τ as a subset of the Cantor set (via characteristic functions) is an analytic (resp. Borel) set. For example, the topology of the Arkhangel’skiĭ-Franklin space is . In this paper we study the complexity, in the sense of the Borel hierarchy, of subspaces of . We show that has subspaces with topologies of arbitrarily high Borel rank and it also has subspaces with a non-Borel topology....