Hurewicz sets of reals without perfect subsets
General Topology
2011-08-08 v5 Logic
Abstract
We show that even for subsets X of the real line which do not contain perfect sets, the Hurewicz property does not imply the property S1(Gamma,Gamma), asserting that for each countable family of open gamma-covers of X, there is a choice function whose image is a gamma-cover of X. This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszynski and Tsaban, and implies that for C_p(X), the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskii's property alpha_2.
Keywords
Cite
@article{arxiv.math/0612148,
title = {Hurewicz sets of reals without perfect subsets},
author = {Dušan Repovš and Boaz Tsaban and Lyubomyr Zdomskyy},
journal= {arXiv preprint arXiv:math/0612148},
year = {2011}
}