2002/08/31 by Tomek Bartoszynski, Boaz Tsaban · 1 citation
Mathematics · #math.LO #math.CA #math.CO #math.GN #msc:37F20 #msc:26A03 #msc:03E75
paper · pdf · doi:10.1090/s0002-9939-05-07997-9
published as Proceedings of the American Mathematical Society 134 (2006), 605--615
arxiv created 2010/10/31 · arxiv updated 2010/11/02
We consider the question, which of the major classes defined by topological diagonalizations of open or Borel covers is hereditary. Many of the classes in the open case are not hereditary already in ZFC, and none of them is provably hereditary. This is contrasted with the Borel case, where some of the classes are provably hereditary. Two of the examples are counter-examples of sizes d and b, respectively, to the Menger and Hurewicz Conjectures, and one of them answers a question of Steprans on perfectly meager sets.