Uniformization and anti-uniformization properties of ladder systems
Countably paracompact, Ladder systems, Normal, Screenable, Uniformizable
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 ω21 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 Clubsuit sign, is considered.
Original Publication Date
DOI of published version
Balogh, Zoltán; Eisworth, Todd; Gruenhage, Gary; Pavlov, Oleg; and Szeptycki, Paul, "Uniformization and anti-uniformization properties of ladder systems" (2004). Faculty Publications. 3147.