Hereditary Topological Diagonalizations and the Menger-hurewicz Conjectures
نویسندگان
چکیده
We consider the question, which of the major classes defined by topological diagonalizations of open or Borel covers is provably, or at least consistently, hereditary. Many of the classes in the open case are not hereditary already in ZFC. We show that none of them is provably hereditary. This is contrasted with the Borel case, where some of the classes are provably hereditary. We also give two ZFC constructions of special witnesses to some classes not being hereditary. These examples are counter-examples of sizes d and b, respectively, to the Menger and Hurewicz Conjectures.
منابع مشابه
Hereditary Topological
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 counterexamples of sizes d and b, res...
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