Uniformization and anti-uniformization properties of ladder systems

Todd Eisworth, et al. "Uniformization and anti-uniformization properties of ladder systems." Fundamenta Mathematicae 181.3 (2004): 189-213. <http://eudml.org/doc/283235>.

@article{ToddEisworth2004,
abstract = {Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness. The existence of a thin, countably metacompact ladder system is used to construct interesting topological spaces: a countably paracompact and nonnormal subspace of ω₁², and a countably paracompact, locally compact screenable space which is not paracompact. Whether the existence of a thin, countably metacompact ladder system is consistent is left open. Finally, the relation between the properties introduced and other well known properties of ladder systems, such as ♣, is considered.},
author = {Todd Eisworth, Gary Gruenhage, Oleg Pavlov, Paul Szeptycki},
journal = {Fundamenta Mathematicae},
keywords = {ladder systems; screenable space; countably paracompact space; normality; weakenings of uniformizability},
language = {eng},
number = {3},
pages = {189-213},
title = {Uniformization and anti-uniformization properties of ladder systems},
url = {http://eudml.org/doc/283235},
volume = {181},
year = {2004},
}

TY - JOUR
AU - Todd Eisworth
AU - Gary Gruenhage
AU - Oleg Pavlov
AU - Paul Szeptycki
TI - Uniformization and anti-uniformization properties of ladder systems
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 3
SP - 189
EP - 213
AB - Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness. The existence of a thin, countably metacompact ladder system is used to construct interesting topological spaces: a countably paracompact and nonnormal subspace of ω₁², and a countably paracompact, locally compact screenable space which is not paracompact. Whether the existence of a thin, countably metacompact ladder system is consistent is left open. Finally, the relation between the properties introduced and other well known properties of ladder systems, such as ♣, is considered.
LA - eng
KW - ladder systems; screenable space; countably paracompact space; normality; weakenings of uniformizability
UR - http://eudml.org/doc/283235
ER -