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Combinatorics of open covers (VII): Groupability

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Kočinac L., Scheepers M.

Fundamenta Mathematicae

2003

tom 179

nr 2

131-155

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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1 Fundamenta Mathematicae

1 Kočinac L.

1 Scheepers M.

1 2003

Wyniki wyszukiwania

Combinatorics of open covers (VII): Groupability