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## Fundamenta Mathematicae

2003 | 179 | 2 | 131-155
Tytuł artykułu

### Combinatorics of open covers (VII): Groupability

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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 $C_{p}(X)$.
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Rocznik
Tom
Numer
Strony
131-155
Opis fizyczny
Daty
wydano
2003
Twórcy
• Department of Mathematics, Faculty of Sciences, University of Niš, 18000 Niš, Yugoslavia
autor
• Department of Mathematics, Boise State University, Boise, ID 83725, U.S.A.
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