Combinatorics of open covers (VII): Groupability

• Autorzy: Ljubiša D. R. Kočinac , Marion Scheepers
• Języki publikacji: EN

Abstrakty

EN

We use Ramseyan partition relations to characterize:
∙ the classical covering property of Hurewicz;
∙ the covering property of Gerlits and Nagy;
∙ the combinatorial cardinal numbers 𝔟 and add(ℳ ).
Let X be a $T_{31/2}$-space. In [9] we showed that $C_{p}(X)$ has countable strong fan tightness as well as the Reznichenko property if, and only if, all finite powers of X have the Gerlits-Nagy covering property. Now we show that the following are equivalent:
1. $C_{p}(X)$ has countable fan tightness and the Reznichenko property.
2. All finite powers of X have the Hurewicz property.
We show that for $C_{p}(X)$ the combination of countable fan tightness with the Reznichenko property is characterized by a Ramseyan partition relation. Extending the work in [9], we give an analogous Ramseyan characterization for the combination of countable strong fan tightness with the Reznichenko property on $C_{p}(X)$.

Kategorie tematyczne

• 91A44: Games involving topology or set theory
• 03E02: Partition relations
• 54C35: Function spaces
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 179
• Numer: 2
• Strony: 131-155

Daty

wydano

2003

Twórcy

autor

Ljubiša D. R. Kočinac

• Department of Mathematics, Faculty of Sciences, University of Niš, 18000 Niš, Yugoslavia

autor

Marion Scheepers

• Department of Mathematics, Boise State University, Boise, ID 83725, U.S.A.

Identyfikatory

DOI

10.4064/fm179-2-2