Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures

Details Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures

2002-08-28

arxiv.org/abs/math/0208224v10

Proceedings of the American Mathematical Society 134 (2006), 605--615

Mathematics

Logic

Scientific paper

10.1090/S0002-9939-05-07997-9

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.

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