The gamma - Borel conjecture
Abstract
In this paper we show that it is relatively consistent with ZFC that every gamma-set is countable while not every strong measure zero set is countable. This answers a question of Paul Szeptycki. A set is a gamma-set iff every omega-cover contains a gamma-subcover. An open cover is an omega-cover iff every finite set is covered by some element of the cover. An open cover is a gamma-cover iff every element of the space is in all but finitely many elements of the cover. Gerlits and Nagy proved that every gamma-set has strong measure zero. We also show that is consistent that every strong gamma-set is countable while there exists an uncountable gamma-set. On the other hand every strong measure zero set is countable iff every set with the Rothberger property is countable.
Cite
@article{arxiv.math/0312308,
title = {The gamma - Borel conjecture},
author = {Arnold W. Miller},
journal= {arXiv preprint arXiv:math/0312308},
year = {2007}
}
Comments
LaTex2e, 16 pages