Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures
By Tomek Bartoszynski, Boaz Tsaban. 2002
80 citations recorded by the source corpus.
We consider the question of 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 are provably hereditary. This is in contrast with the Borel case, where some of the classes are provably hereditary. Two of the examples are counter-examples of sizes 0 and b, respectively, to the Menger and Hurewicz Conjectures, and one of them answers a question of Steprans on perfectly meager sets.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f2a6a7c61a07275c592297e56f595ea79ab01c64
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In Algebra and Number Theory
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Citations in the corpus
- MENGER'S AND HUREWICZ'S PROBLEMS: SOLUTIONS FROM "THE BOOK" AND REFINEMENTS (2009, methodology): “Thus, the Continuum Hypothesis implies the failure of Hurewicz’s Conjecture.”
- A semifilter approach to selection principles (2004, background): “spaces having the Menger property appeared to be much wider than the class of σ-compact spaces (see [5], [7], [10] and many others), but it has interesting properties itself and poses a number of open questions.”