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Uniformization and anti-uniformization properties of ladder systems

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Eisworth T., Gruenhage G., Pavlov O., Szeptycki P.

Fundamenta Mathematicae

2004

tom 181

nr 3

189-213

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Eisworth T.

1 Gruenhage G.

1 Pavlov O.

1 Szeptycki P.

1 2004

Wyniki wyszukiwania

Uniformization and anti-uniformization properties of ladder systems