Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures
Logic
2010-11-02 v9 Classical Analysis and ODEs
Combinatorics
General Topology
Abstract
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.
Cite
@article{arxiv.math/0208224,
title = {Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures},
author = {Tomek Bartoszynski and Boaz Tsaban},
journal= {arXiv preprint arXiv:math/0208224},
year = {2010}
}